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Math Problems
Calculus
Evaluate definite integrals using the chain rule
∫
t
e
t
1
+
e
2
t
d
t
\int \frac{t e^{t}}{1+e^{2 t}} d t
∫
1
+
e
2
t
t
e
t
d
t
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∫
1
x
3
+
1
d
x
\int \frac{1}{x^{3}+1} \, dx
∫
x
3
+
1
1
d
x
Get tutor help
Select all the expressions that are equivalent to
6
−
4
×
6
−
4
6^{-4} \times 6^{-4}
6
−
4
×
6
−
4
.
\newline
Multi-select Choices:
\newline
(A)
1
6
16
\frac{1}{6^{16}}
6
16
1
\newline
(B)
6
16
6^{16}
6
16
\newline
(C)
1
6
−
8
\frac{1}{6^{-8}}
6
−
8
1
\newline
(D)
6
−
8
6^{-8}
6
−
8
Get tutor help
∫
x
1
3
cos
(
x
2
/
3
,
8
)
d
x
\int x^{\frac{1}{3}} \cos \left(x^{2 / 3}, 8\right) d x
∫
x
3
1
cos
(
x
2/3
,
8
)
d
x
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∫
0
π
x
sin
x
1
+
cos
2
x
d
x
\int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x
∫
0
π
1
+
c
o
s
2
x
x
s
i
n
x
d
x
Get tutor help
1
1
1
. Noma'lum burchakni toping (
1
1
1
-rasm).
\newline
2
2
2
. Uchburchakning tashqi burchagi
12
0
∘
120^{\circ}
12
0
∘
bo'lib, unga qo'shni bo'Imagan ichki burchaklari
1
1
1
:
2
2
2
nisbatda bo'lsa, uchburchakning burchaklarini toping.
\newline
3
3
3
. Agar
2
2
2
-rasmda
∠
A
C
B
=
9
0
∘
,
C
D
=
B
D
\angle A C B=90^{\circ}, C D=B D
∠
A
CB
=
9
0
∘
,
C
D
=
B
D
va
A
B
=
24
s
m
A B=24 \mathrm{sm}
A
B
=
24
sm
bo
Get tutor help
∫
0
2
2
x
(
x
2
2
+
3
)
5
d
x
\int_{0}^{2} 2 x\left(\frac{x^{2}}{2}+3\right)^{5} d x
∫
0
2
2
x
(
2
x
2
+
3
)
5
d
x
Get tutor help
savasrealize.com/dashboard/classes/
64
64
64
c
0
0
0
d
3292
3292
3292
e
855
855
855
b
71
71
71
a
5
5
5
d
56
56
56
e
7
7
7
e/details/assignments/
0726
0726
0726
fcb
73
73
73
c
794
794
794
ad
696
696
696
c
\newline
Maps
\newline
SCHLOETER HOMEROOM
502
502
502
8
8
8
(A)
\newline
Topic
8
8
8
: Online Assessment Copy
1
1
1
\newline
A. Select all the expressions that show breaking the addends
7
5
12
7 \frac{5}{12}
7
12
5
and
11
2
3
11 \frac{2}{3}
11
3
2
apart to make a whole.
\newline
7
+
5
12
+
11
+
2
3
7+\frac{5}{12}+11+\frac{2}{3}
7
+
12
5
+
11
+
3
2
\newline
7
+
5
12
+
8
12
+
11
7+\frac{5}{12}+\frac{8}{12}+11
7
+
12
5
+
12
8
+
11
\newline
7
+
5
12
+
7
12
+
11
1
12
7+\frac{5}{12}+\frac{7}{12}+11 \frac{1}{12}
7
+
12
5
+
12
7
+
11
12
1
\newline
7
+
5
12
+
5
12
+
11
3
12
7+\frac{5}{12}+\frac{5}{12}+11 \frac{3}{12}
7
+
12
5
+
12
5
+
11
12
3
\newline
7
+
1
12
+
4
12
+
8
12
+
11
7+\frac{1}{12}+\frac{4}{12}+\frac{8}{12}+11
7
+
12
1
+
12
4
+
12
8
+
11
Get tutor help
Let
H
(
x
)
=
3
x
+
∫
1
x
2
g
(
x
)
d
x
H(x)=3 x+\int_{1}^{x^{2}} g(x) d x
H
(
x
)
=
3
x
+
∫
1
x
2
g
(
x
)
d
x
\newline
(c) Find
H
′
(
2
)
H^{\prime}(2)
H
′
(
2
)
and
H
′
′
(
2
)
H^{\prime \prime}(2)
H
′′
(
2
)
.
Get tutor help
∫
0
π
2
sin
2
θ
(
1
+
cos
θ
)
2
d
θ
\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} \theta}{(1+\cos \theta)^{2}} d \theta
∫
0
2
π
(
1
+
c
o
s
θ
)
2
s
i
n
2
θ
d
θ
Get tutor help
iolve the Definite Integral:
\newline
∫
−
6
14
10
x
4
+
12
x
3
−
16
x
2
−
9
x
+
15
d
x
\int_{-6}^{14} 10 x^{4}+12 x^{3}-16 x^{2}-9 x+15 d x
∫
−
6
14
10
x
4
+
12
x
3
−
16
x
2
−
9
x
+
15
d
x
Get tutor help
Solve the Definite Integral:
\newline
∫
−
6
14
10
x
4
+
12
x
3
−
16
x
2
−
9
x
+
15
d
x
\int_{-6}^{14} 10 x^{4}+12 x^{3}-16 x^{2}-9 x+15 d x
∫
−
6
14
10
x
4
+
12
x
3
−
16
x
2
−
9
x
+
15
d
x
\newline
Section
5
5
5
.
4
4
4
Get tutor help
2
2
2
.
∫
0
1
2
π
2
cos
2
t
d
t
\int_{0}^{\frac{1}{2} \pi^{2}} \cos \sqrt{2 t} d t
∫
0
2
1
π
2
cos
2
t
d
t
Get tutor help
If
∫
3
14
f
(
x
)
d
x
=
68
\int_{3}^{14} f(x) d x=68
∫
3
14
f
(
x
)
d
x
=
68
and
∫
11
14
f
(
x
)
d
x
=
10
\int_{11}^{14} f(x) d x=10
∫
11
14
f
(
x
)
d
x
=
10
, calculate
∫
3
11
f
(
x
)
d
x
\int_{3}^{11} f(x) d x
∫
3
11
f
(
x
)
d
x
Get tutor help
∫
−
2
2
(
(
x
3
cos
x
2
+
1
2
)
4
−
x
2
d
x
\int_{-2}^{2}\left(\left(x^{3} \cos \frac{x}{2}+\frac{1}{2}\right) \sqrt{4-x^{2}} d x\right.
∫
−
2
2
(
(
x
3
cos
2
x
+
2
1
)
4
−
x
2
d
x
Get tutor help
find
∫
0
1
(
f
(
x
)
−
g
(
x
)
)
d
x
\int_{0}^{1}(f(x)-g(x))\,dx
∫
0
1
(
f
(
x
)
−
g
(
x
))
d
x
, if
∫
0
1
(
f
(
x
)
−
2
g
(
x
)
)
d
x
=
6
\int_{0}^{1}(f(x)-2g(x))\,dx=6
∫
0
1
(
f
(
x
)
−
2
g
(
x
))
d
x
=
6
,
∫
0
1
(
2
f
(
x
)
+
2
g
(
x
)
)
d
x
=
9
\int_{0}^{1}(2f(x)+2g(x))\,dx=9
∫
0
1
(
2
f
(
x
)
+
2
g
(
x
))
d
x
=
9
Get tutor help
Calculate the definite integral of the function
f
(
x
)
=
2
x
f(x) = 2x
f
(
x
)
=
2
x
from
x
=
1
x = 1
x
=
1
to
x
=
3
x = 3
x
=
3
.
Get tutor help
∫
0
1
cos
π
1
−
x
⋅
d
x
(
1
−
x
)
2
\int_{0}^{1} \cos \frac{\pi}{1-x} \cdot \frac{d x}{(1-x)^{2}}
∫
0
1
cos
1
−
x
π
⋅
(
1
−
x
)
2
d
x
.
Get tutor help
Вычислить несобственный интеграл или установить его расходимость
\newline
∫
0
1
cos
π
1
−
x
⋅
d
x
(
1
−
x
)
2
\int_{0}^{1} \cos \frac{\pi}{1-x} \cdot \frac{d x}{(1-x)^{2}}
∫
0
1
cos
1
−
x
π
⋅
(
1
−
x
)
2
d
x
Get tutor help
∫
0
4
x
1
+
2
x
d
x
\int_{0}^{4} \frac{x}{\sqrt{1+2 x}} d x
∫
0
4
1
+
2
x
x
d
x
Get tutor help
1
1
1
. Вычислить определённый интеграл
\newline
∫
0
3
4
d
x
(
x
+
1
)
x
2
+
1
\int_{0}^{\frac{3}{4}} \frac{d x}{(x+1) \sqrt{x^{2}+1}}
∫
0
4
3
(
x
+
1
)
x
2
+
1
d
x
Get tutor help
ntegration and finding the value of
C
\mathrm{C}
C
Worksheet
\newline
For each of the following problems, integrate and then find the
\newline
∫
12
s
5
+
5
s
4
d
s
\int 12 s^{5}+5 s^{4} d s
∫
12
s
5
+
5
s
4
d
s
\newline
at the point
(
1
,
5
)
(1,5)
(
1
,
5
)
.
Get tutor help
∫
(
1
+
x
/
2
)
8
d
x
\int(1+x/2)^{8}\,dx
∫
(
1
+
x
/2
)
8
d
x
Get tutor help
1
1
1
.)
∫
(
1
+
x
/
2
)
8
d
x
\int(1+x / 2)^{8} d x
∫
(
1
+
x
/2
)
8
d
x
Get tutor help
∫
1
5
2
ln
(
x
2
+
3
)
(
x
2
+
3
)
d
x
\int_{1}^{\sqrt{5}} \frac{2 \ln \left(x^{2}+3\right)}{\left(x^{2}+3\right)} d x
∫
1
5
(
x
2
+
3
)
2
l
n
(
x
2
+
3
)
d
x
Get tutor help
∫
1
5
2
ln
(
x
2
+
7
)
x
2
+
2
d
x
\int_{1}^{\sqrt{5}} \frac{2 \ln \left(x^{2}+7\right)}{x^{2}+2} d x
∫
1
5
x
2
+
2
2
l
n
(
x
2
+
7
)
d
x
Get tutor help
−
∫
1
5
1
−
2
ln
(
x
2
+
3
)
(
x
2
+
3
)
-\int_{1}^{\sqrt{\mathbf{5}}} \frac{1-2 \ln \left(x^{2}+3\right)}{\left(x^{2}+3\right)}
−
∫
1
5
(
x
2
+
3
)
1
−
2
l
n
(
x
2
+
3
)
Get tutor help
−
∫
−
1
3
1
−
2
ln
x
2
+
3
(
x
2
+
3
)
-\int_{-1}^{\sqrt{3}} \frac{1-2 \ln x^{2}+3}{\left(x^{2}+3\right)}
−
∫
−
1
3
(
x
2
+
3
)
1
−
2
l
n
x
2
+
3
Get tutor help
Find
∫
1
−
x
2
−
6
x
+
40
d
x
\int \frac{1}{\sqrt{-x^{2}-6 x+40}} d x
∫
−
x
2
−
6
x
+
40
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
14
arctan
(
x
+
3
7
)
+
C
\frac{1}{14} \arctan \left(\frac{x+3}{7}\right)+C
14
1
arctan
(
7
x
+
3
)
+
C
\newline
(B)
1
14
arcsin
(
x
+
3
7
)
+
C
\frac{1}{14} \arcsin \left(\frac{x+3}{7}\right)+C
14
1
arcsin
(
7
x
+
3
)
+
C
\newline
(c)
arctan
(
x
+
3
7
)
+
C
\arctan \left(\frac{x+3}{7}\right)+C
arctan
(
7
x
+
3
)
+
C
\newline
()
arcsin
(
x
+
3
7
)
+
C
\arcsin \left(\frac{x+3}{7}\right)+C
arcsin
(
7
x
+
3
)
+
C
Get tutor help
Find
∫
1
−
x
2
−
4
x
+
21
d
x
\int \frac{1}{\sqrt{-x^{2}-4 x+21}} d x
∫
−
x
2
−
4
x
+
21
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
5
arctan
(
x
+
2
5
)
+
C
\frac{1}{5} \arctan \left(\frac{x+2}{5}\right)+C
5
1
arctan
(
5
x
+
2
)
+
C
\newline
(B)
1
5
arcsin
(
x
+
2
5
)
+
C
\frac{1}{5} \arcsin \left(\frac{x+2}{5}\right)+C
5
1
arcsin
(
5
x
+
2
)
+
C
\newline
(c)
arctan
(
x
+
2
5
)
+
C
\arctan \left(\frac{x+2}{5}\right)+C
arctan
(
5
x
+
2
)
+
C
\newline
(D)
arcsin
(
x
+
2
5
)
+
C
\arcsin \left(\frac{x+2}{5}\right)+C
arcsin
(
5
x
+
2
)
+
C
Get tutor help
Evaluate the integral
∫
x
−
5
−
2
x
+
2
d
x
\int \frac{x-5}{-2 x+2} d x
∫
−
2
x
+
2
x
−
5
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
x
−
2
ln
∣
x
−
1
∣
+
C
\frac{1}{2} x-2 \ln |x-1|+C
2
1
x
−
2
ln
∣
x
−
1∣
+
C
\newline
(B)
1
2
x
+
2
ln
∣
x
−
1
∣
+
C
\frac{1}{2} x+2 \ln |x-1|+C
2
1
x
+
2
ln
∣
x
−
1∣
+
C
\newline
(C)
−
1
2
x
−
2
ln
∣
x
−
1
∣
+
C
-\frac{1}{2} x-2 \ln |x-1|+C
−
2
1
x
−
2
ln
∣
x
−
1∣
+
C
\newline
(D)
−
1
2
x
+
2
ln
∣
x
−
1
∣
+
C
-\frac{1}{2} x+2 \ln |x-1|+C
−
2
1
x
+
2
ln
∣
x
−
1∣
+
C
Get tutor help
Evaluate the integral
∫
x
−
1
2
x
+
4
d
x
\int \frac{x-1}{2 x+4} d x
∫
2
x
+
4
x
−
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
x
−
1
2
ln
∣
x
+
2
∣
+
C
\frac{1}{2} x-\frac{1}{2} \ln |x+2|+C
2
1
x
−
2
1
ln
∣
x
+
2∣
+
C
\newline
(B)
1
2
x
−
ln
∣
x
+
2
∣
+
C
\frac{1}{2} x-\ln |x+2|+C
2
1
x
−
ln
∣
x
+
2∣
+
C
\newline
(C)
1
2
x
−
3
2
ln
∣
x
+
2
∣
+
C
\frac{1}{2} x-\frac{3}{2} \ln |x+2|+C
2
1
x
−
2
3
ln
∣
x
+
2∣
+
C
\newline
(D)
1
2
x
−
2
ln
∣
x
+
2
∣
+
C
\frac{1}{2} x-2 \ln |x+2|+C
2
1
x
−
2
ln
∣
x
+
2∣
+
C
Get tutor help
Evaluate
∫
x
3
−
1
x
+
2
d
x
\int \frac{x^{3}-1}{x+2} d x
∫
x
+
2
x
3
−
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
x
3
3
−
x
2
+
4
x
−
7
ln
∣
x
+
2
∣
+
C
\frac{x^{3}}{3}-x^{2}+4 x-7 \ln |x+2|+C
3
x
3
−
x
2
+
4
x
−
7
ln
∣
x
+
2∣
+
C
\newline
(B)
x
3
3
−
2
x
2
+
4
x
−
7
ln
∣
x
+
2
∣
+
C
\frac{x^{3}}{3}-2 x^{2}+4 x-7 \ln |x+2|+C
3
x
3
−
2
x
2
+
4
x
−
7
ln
∣
x
+
2∣
+
C
\newline
(C)
x
3
3
−
x
2
+
4
x
−
9
ln
∣
x
+
2
∣
+
C
\frac{x^{3}}{3}-x^{2}+4 x-9 \ln |x+2|+C
3
x
3
−
x
2
+
4
x
−
9
ln
∣
x
+
2∣
+
C
\newline
(D)
x
3
3
−
2
x
2
+
4
x
−
9
ln
∣
x
+
2
∣
+
C
\frac{x^{3}}{3}-2 x^{2}+4 x-9 \ln |x+2|+C
3
x
3
−
2
x
2
+
4
x
−
9
ln
∣
x
+
2∣
+
C
Get tutor help
Evaluate
∫
x
6
+
2
x
4
+
6
x
−
9
x
3
+
3
d
x
\int \frac{x^{6}+2 x^{4}+6 x-9}{x^{3}+3} d x
∫
x
3
+
3
x
6
+
2
x
4
+
6
x
−
9
d
x
\newline
Choose
1
1
1
answer:
\newline
(A)
x
4
4
+
x
2
−
3
x
+
C
\frac{x^{4}}{4}+x^{2}-3 x+C
4
x
4
+
x
2
−
3
x
+
C
\newline
(B)
x
4
4
+
x
2
−
9
x
+
C
\frac{x^{4}}{4}+x^{2}-9 x+C
4
x
4
+
x
2
−
9
x
+
C
\newline
(C)
x
4
4
+
3
x
2
+
3
x
+
C
\frac{x^{4}}{4}+3 x^{2}+3 x+C
4
x
4
+
3
x
2
+
3
x
+
C
\newline
(D)
x
4
4
+
x
2
+
3
x
+
C
\frac{x^{4}}{4}+x^{2}+3 x+C
4
x
4
+
x
2
+
3
x
+
C
Get tutor help
Evaluate the integral
∫
3
x
+
4
x
+
3
d
x
\int \frac{3 x+4}{x+3} d x
∫
x
+
3
3
x
+
4
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
=
9
x
−
4
ln
∣
x
+
3
∣
+
C
=9 x-4 \ln |x+3|+C
=
9
x
−
4
ln
∣
x
+
3∣
+
C
\newline
(B)
=
3
x
−
5
ln
∣
x
+
3
∣
+
C
=3 x-5 \ln |x+3|+C
=
3
x
−
5
ln
∣
x
+
3∣
+
C
\newline
(C)
=
3
x
+
5
ln
∣
x
+
3
∣
+
C
=3 x+5 \ln |x+3|+C
=
3
x
+
5
ln
∣
x
+
3∣
+
C
\newline
(D)
=
9
x
−
5
ln
∣
x
+
3
∣
+
C
=9 x-5 \ln |x+3|+C
=
9
x
−
5
ln
∣
x
+
3∣
+
C
Get tutor help
Evaluate the integral
∫
2
x
+
1
x
+
2
d
x
\int \frac{2 x+1}{x+2} d x
∫
x
+
2
2
x
+
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
−
3
ln
∣
x
+
2
∣
+
C
2 x-3 \ln |x+2|+C
2
x
−
3
ln
∣
x
+
2∣
+
C
\newline
(B)
ln
∣
x
+
2
∣
+
C
\ln |x+2|+C
ln
∣
x
+
2∣
+
C
\newline
(C)
x
+
ln
∣
2
x
+
1
∣
+
C
x+\ln |2 x+1|+C
x
+
ln
∣2
x
+
1∣
+
C
\newline
(D)
2
x
−
ln
∣
x
+
2
∣
+
C
2 x-\ln |x+2|+C
2
x
−
ln
∣
x
+
2∣
+
C
Get tutor help
Find
∫
1
−
x
2
+
12
x
−
32
d
x
\int \frac{1}{\sqrt{-x^{2}+12 x-32}} d x
∫
−
x
2
+
12
x
−
32
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
arcsin
(
x
−
6
2
)
+
C
\arcsin \left(\frac{x-6}{2}\right)+C
arcsin
(
2
x
−
6
)
+
C
\newline
(B)
1
12
arctan
(
x
−
6
2
)
+
C
\frac{1}{12} \arctan \left(\frac{x-6}{2}\right)+C
12
1
arctan
(
2
x
−
6
)
+
C
\newline
(C)
1
12
arcsin
(
x
−
6
2
)
+
C
\frac{1}{12} \arcsin \left(\frac{x-6}{2}\right)+C
12
1
arcsin
(
2
x
−
6
)
+
C
\newline
(D)
arctan
(
x
−
6
2
)
+
C
\arctan \left(\frac{x-6}{2}\right)+C
arctan
(
2
x
−
6
)
+
C
Get tutor help
Evaluate
∫
x
3
+
x
x
+
1
d
x
\int \frac{x^{3}+x}{x+1} d x
∫
x
+
1
x
3
+
x
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
x
3
3
−
x
2
2
+
2
x
−
2
ln
∣
x
+
1
∣
+
C
\frac{x^{3}}{3}-\frac{x^{2}}{2}+2 x-2 \ln |x+1|+C
3
x
3
−
2
x
2
+
2
x
−
2
ln
∣
x
+
1∣
+
C
\newline
(B)
x
3
3
+
2
x
−
2
ln
∣
x
+
1
∣
+
C
\frac{x^{3}}{3}+2 x-2 \ln |x+1|+C
3
x
3
+
2
x
−
2
ln
∣
x
+
1∣
+
C
\newline
(C)
x
3
3
−
x
2
2
+
2
x
+
2
ln
∣
x
+
1
∣
+
C
\frac{x^{3}}{3}-\frac{x^{2}}{2}+2 x+2 \ln |x+1|+C
3
x
3
−
2
x
2
+
2
x
+
2
ln
∣
x
+
1∣
+
C
\newline
(D)
x
3
3
+
x
2
+
2
x
+
2
ln
∣
x
+
1
∣
+
C
\frac{x^{3}}{3}+x^{2}+2 x+2 \ln |x+1|+C
3
x
3
+
x
2
+
2
x
+
2
ln
∣
x
+
1∣
+
C
Get tutor help
Evaluate the integral
∫
x
−
2
3
x
+
6
d
x
\int \frac{x-2}{3 x+6} d x
∫
3
x
+
6
x
−
2
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
x
−
4
ln
∣
x
+
2
∣
3
+
C
\frac{1}{2} x-\frac{4 \ln |x+2|}{3}+C
2
1
x
−
3
4
l
n
∣
x
+
2∣
+
C
\newline
(B)
1
2
x
+
4
ln
∣
x
+
2
∣
3
+
C
\frac{1}{2} x+\frac{4 \ln |x+2|}{3}+C
2
1
x
+
3
4
l
n
∣
x
+
2∣
+
C
\newline
(C)
1
3
x
−
4
ln
∣
x
+
2
∣
3
+
C
\frac{1}{3} x-\frac{4 \ln |x+2|}{3}+C
3
1
x
−
3
4
l
n
∣
x
+
2∣
+
C
\newline
(D)
1
3
x
+
4
ln
∣
x
+
2
∣
3
+
C
\frac{1}{3} x+\frac{4 \ln |x+2|}{3}+C
3
1
x
+
3
4
l
n
∣
x
+
2∣
+
C
Get tutor help
Evaluate the integral
∫
x
+
4
2
x
+
6
d
x
\int \frac{x+4}{2 x+6} d x
∫
2
x
+
6
x
+
4
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
−
ln
∣
2
x
+
6
∣
2
+
C
2 x-\frac{\ln |2 x+6|}{2}+C
2
x
−
2
l
n
∣2
x
+
6∣
+
C
\newline
(B)
1
2
x
−
ln
∣
2
x
+
6
∣
2
+
C
\frac{1}{2} x-\frac{\ln |2 x+6|}{2}+C
2
1
x
−
2
l
n
∣2
x
+
6∣
+
C
\newline
(C)
2
x
+
ln
∣
2
x
+
6
∣
+
C
2 x+\ln |2 x+6|+C
2
x
+
ln
∣2
x
+
6∣
+
C
\newline
(D)
1
2
x
+
ln
∣
2
x
+
6
∣
2
+
C
\frac{1}{2} x+\frac{\ln |2 x+6|}{2}+C
2
1
x
+
2
l
n
∣2
x
+
6∣
+
C
Get tutor help
Evaluate
∫
2
x
3
+
7
x
2
+
2
x
+
9
2
x
+
3
d
x
\int \frac{2 x^{3}+7 x^{2}+2 x+9}{2 x+3} d x
∫
2
x
+
3
2
x
3
+
7
x
2
+
2
x
+
9
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
x
3
3
+
x
2
−
2
x
+
15
ln
∣
2
x
+
3
∣
2
+
C
\frac{x^{3}}{3}+x^{2}-2 x+\frac{15 \ln |2 x+3|}{2}+C
3
x
3
+
x
2
−
2
x
+
2
15
l
n
∣2
x
+
3∣
+
C
\newline
(B)
x
3
3
+
x
2
−
2
x
+
5
ln
∣
2
x
+
3
∣
2
+
C
\frac{x^{3}}{3}+x^{2}-2 x+\frac{5 \ln |2 x+3|}{2}+C
3
x
3
+
x
2
−
2
x
+
2
5
l
n
∣2
x
+
3∣
+
C
\newline
(C)
x
3
3
+
x
2
2
−
2
x
+
15
ln
∣
2
x
+
3
∣
2
+
C
\frac{x^{3}}{3}+\frac{x^{2}}{2}-2 x+\frac{15 \ln |2 x+3|}{2}+C
3
x
3
+
2
x
2
−
2
x
+
2
15
l
n
∣2
x
+
3∣
+
C
\newline
(D)
x
3
3
+
x
2
2
−
2
x
+
5
ln
∣
2
x
+
3
∣
2
+
C
\frac{x^{3}}{3}+\frac{x^{2}}{2}-2 x+\frac{5 \ln |2 x+3|}{2}+C
3
x
3
+
2
x
2
−
2
x
+
2
5
l
n
∣2
x
+
3∣
+
C
Get tutor help
Find
∫
1
x
2
−
6
x
+
13
d
x
\int \frac{1}{x^{2}-6 x+13} d x
∫
x
2
−
6
x
+
13
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
arcsin
(
x
−
3
2
)
+
C
\frac{1}{2} \arcsin \left(\frac{x-3}{2}\right)+C
2
1
arcsin
(
2
x
−
3
)
+
C
\newline
(B)
1
4
arcsin
(
x
−
3
2
)
+
C
\frac{1}{4} \arcsin \left(\frac{x-3}{2}\right)+C
4
1
arcsin
(
2
x
−
3
)
+
C
\newline
(C)
1
2
arctan
(
x
−
3
2
)
+
C
\frac{1}{2} \arctan \left(\frac{x-3}{2}\right)+C
2
1
arctan
(
2
x
−
3
)
+
C
\newline
(D)
1
4
arctan
(
x
−
3
2
)
+
C
\frac{1}{4} \arctan \left(\frac{x-3}{2}\right)+C
4
1
arctan
(
2
x
−
3
)
+
C
Get tutor help
Find
∫
1
−
x
2
+
10
x
+
11
d
x
\int \frac{1}{\sqrt{-x^{2}+10 x+11}} d x
∫
−
x
2
+
10
x
+
11
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
6
arctan
(
x
−
5
6
)
+
C
\frac{1}{6} \arctan \left(\frac{x-5}{6}\right)+C
6
1
arctan
(
6
x
−
5
)
+
C
\newline
(B)
1
6
arcsin
(
x
−
5
6
)
+
C
\frac{1}{6} \arcsin \left(\frac{x-5}{6}\right)+C
6
1
arcsin
(
6
x
−
5
)
+
C
\newline
(C)
arcsin
(
x
−
5
6
)
+
C
\arcsin \left(\frac{x-5}{6}\right)+C
arcsin
(
6
x
−
5
)
+
C
\newline
(D)
arctan
(
x
−
5
6
)
+
C
\arctan \left(\frac{x-5}{6}\right)+C
arctan
(
6
x
−
5
)
+
C
Get tutor help
Find
∫
1
3
x
2
+
6
x
+
78
d
x
\int \frac{1}{3 x^{2}+6 x+78} d x
∫
3
x
2
+
6
x
+
78
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
arctan
(
x
+
1
5
)
+
C
\arctan \left(\frac{x+1}{5}\right)+C
arctan
(
5
x
+
1
)
+
C
\newline
(B)
arcsin
(
x
+
1
5
)
+
C
\arcsin \left(\frac{x+1}{5}\right)+C
arcsin
(
5
x
+
1
)
+
C
\newline
(c)
1
15
arctan
(
x
+
1
5
)
+
C
\frac{1}{15} \arctan \left(\frac{x+1}{5}\right)+C
15
1
arctan
(
5
x
+
1
)
+
C
\newline
(D)
1
15
arcsin
(
x
+
1
5
)
+
C
\frac{1}{15} \arcsin \left(\frac{x+1}{5}\right)+C
15
1
arcsin
(
5
x
+
1
)
+
C
Get tutor help
Find
∫
1
x
2
+
8
x
+
52
d
x
\int \frac{1}{x^{2}+8 x+52} d x
∫
x
2
+
8
x
+
52
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
6
arcsin
(
x
+
4
6
)
+
C
\frac{1}{6} \arcsin \left(\frac{x+4}{6}\right)+C
6
1
arcsin
(
6
x
+
4
)
+
C
\newline
(B)
arctan
(
x
+
4
6
)
+
C
\arctan \left(\frac{x+4}{6}\right)+C
arctan
(
6
x
+
4
)
+
C
\newline
(C)
1
6
arctan
(
x
+
4
6
)
+
C
\frac{1}{6} \arctan \left(\frac{x+4}{6}\right)+C
6
1
arctan
(
6
x
+
4
)
+
C
\newline
(D)
arcsin
(
x
+
4
6
)
+
C
\arcsin \left(\frac{x+4}{6}\right)+C
arcsin
(
6
x
+
4
)
+
C
Get tutor help
Find
∫
1
−
x
2
−
14
x
−
48
d
x
\int \frac{1}{\sqrt{-x^{2}-14 x-48}} d x
∫
−
x
2
−
14
x
−
48
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
arctan
(
x
+
7
2
)
+
C
\frac{1}{2} \arctan \left(\frac{x+7}{2}\right)+C
2
1
arctan
(
2
x
+
7
)
+
C
\newline
(B)
arcsin
(
x
+
7
)
+
C
\arcsin (x+7)+C
arcsin
(
x
+
7
)
+
C
\newline
(C)
arctan
(
x
+
7
)
+
C
\arctan (x+7)+C
arctan
(
x
+
7
)
+
C
\newline
(D)
1
2
arcsin
(
x
+
7
2
)
+
C
\frac{1}{2} \arcsin \left(\frac{x+7}{2}\right)+C
2
1
arcsin
(
2
x
+
7
)
+
C
Get tutor help
Find
∫
1
x
2
−
14
x
+
58
d
x
\int \frac{1}{x^{2}-14 x+58} d x
∫
x
2
−
14
x
+
58
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
21
arcsin
(
x
−
7
3
)
+
C
\frac{1}{21} \arcsin \left(\frac{x-7}{3}\right)+C
21
1
arcsin
(
3
x
−
7
)
+
C
\newline
(B)
1
21
arctan
(
x
−
7
3
)
+
C
\frac{1}{21} \arctan \left(\frac{x-7}{3}\right)+C
21
1
arctan
(
3
x
−
7
)
+
C
\newline
(C)
1
3
arctan
(
x
−
7
3
)
+
C
\frac{1}{3} \arctan \left(\frac{x-7}{3}\right)+C
3
1
arctan
(
3
x
−
7
)
+
C
\newline
(D)
1
3
arcsin
(
x
−
7
3
)
+
C
\frac{1}{3} \arcsin \left(\frac{x-7}{3}\right)+C
3
1
arcsin
(
3
x
−
7
)
+
C
Get tutor help
Find
∫
1
x
2
+
10
x
+
41
d
x
\int \frac{1}{x^{2}+10 x+41} d x
∫
x
2
+
10
x
+
41
1
d
x
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
4
arctan
(
x
+
5
4
)
+
C
\frac{1}{4} \arctan \left(\frac{x+5}{4}\right)+C
4
1
arctan
(
4
x
+
5
)
+
C
\newline
(B)
1
4
arcsin
(
x
+
5
4
)
+
C
\frac{1}{4} \arcsin \left(\frac{x+5}{4}\right)+C
4
1
arcsin
(
4
x
+
5
)
+
C
\newline
(C)
1
20
arcsin
(
x
+
5
4
)
+
C
\frac{1}{20} \arcsin \left(\frac{x+5}{4}\right)+C
20
1
arcsin
(
4
x
+
5
)
+
C
\newline
(D)
1
20
arctan
(
x
+
5
4
)
+
C
\frac{1}{20} \arctan \left(\frac{x+5}{4}\right)+C
20
1
arctan
(
4
x
+
5
)
+
C
Get tutor help
g
(
x
)
=
∫
1
x
2
t
+
7
d
t
g(x)=\int_{1}^{x} \sqrt{2 t+7} d t
g
(
x
)
=
∫
1
x
2
t
+
7
d
t
\newline
g
′
(
9
)
=
g^{\prime}(9)=
g
′
(
9
)
=
Get tutor help
g
(
x
)
=
∫
0
x
10
t
+
1
d
t
g(x)=\int_{0}^{x} \sqrt{10 t+1} d t
g
(
x
)
=
∫
0
x
10
t
+
1
d
t
\newline
g
′
(
8
)
=
g^{\prime}(8)=
g
′
(
8
)
=
Get tutor help
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