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Math Problems
Calculus
Evaluate definite integrals using the chain rule
∫
1
2
d
x
2
−
3
x
\int_{1}^{2} \frac{d x}{2-3 x}
∫
1
2
2
−
3
x
d
x
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∫
0
π
2
(
2
sin
x
+
cos
x
)
2
d
x
\int_{0}^{\frac{\pi}{2}}(2 \sin x+\cos x)^{2} d x
∫
0
2
π
(
2
sin
x
+
cos
x
)
2
d
x
Get tutor help
Jika anda membangun interval kepercayaan untuk rata-rata dengan tingkat kepercayaan
95
%
95\%
95%
berdasarkan data sampel
n
=
25
n = 25
n
=
25
dan simpangan baku sampel
s
=
0
,
05
s =0,05
s
=
0
,
05
, maka nilai kritis akan menjadi ?
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What is the coefficient of the
x
4
y
3
x^{4} y^{3}
x
4
y
3
term in the expansion of
(
x
−
2
y
)
7
(x-2 y)^{7}
(
x
−
2
y
)
7
?
\newline
560
560
560
\newline
35
35
35
\newline
−
8
-8
−
8
\newline
−
280
-280
−
280
Get tutor help
∫
0
π
∫
0
cos
y
x
sin
y
d
x
d
y
\int_{0}^{\pi} \int_{0}^{\cos y} x \sin y d x d y
∫
0
π
∫
0
c
o
s
y
x
sin
y
d
x
d
y
Get tutor help
th Grade
\newline
Fill in the missing values:
\newline
R
P
R P
RP
\newline
\begin{tabular}{|c|c|}
\newline
\hline SPRITE (C) & JUICE (C) \\
\newline
\hline
3
3
3
& \\
\newline
\hline
5
5
5
&
15
15
15
\\
\newline
\hline &
24
24
24
\\
\newline
\hline
12
12
12
& \\
\newline
\hline
\newline
\end{tabular}
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∫
(
3
x
2
+
4
x
−
11
x
)
d
x
\int\left(3 x^{2}+4 x-\frac{11}{x}\right) d x
∫
(
3
x
2
+
4
x
−
x
11
)
d
x
Get tutor help
∫
x
4
+
1
x
2
x
4
−
1
d
x
\int \frac{x^{4}+1}{x^{2} \sqrt{x^{4}-1}} d x
∫
x
2
x
4
−
1
x
4
+
1
d
x
Get tutor help
∫
x
4
+
1
x
2
x
4
−
1
d
x
∣
…
\left.\int \frac{x^{4}+1}{x^{2} \sqrt{x^{4}-1}} d x \right\rvert\, \ldots
∫
x
2
x
4
−
1
x
4
+
1
d
x
∣
∣
…
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2
2
−
4
2^{2-4}
2
2
−
4
(
1
1
1
)
I
y
=
∫
cot
4
x
d
x
I_{y}=\int \cot ^{4} x d x
I
y
=
∫
cot
4
x
d
x
\newline
(
2
2
2
)
I
2
,
3
=
∫
x
2
(
ln
x
)
3
d
x
I_{2,3}=\int x^{2}(\ln x)^{3} d x
I
2
,
3
=
∫
x
2
(
ln
x
)
3
d
x
\newline
29
29
29
−
4
-4
−
4
(
1
1
1
)
∫
d
x
x
2
+
4
x
+
8
\int \frac{d x}{x^{2}+4 x+8}
∫
x
2
+
4
x
+
8
d
x
\newline
(
2
2
2
)
∫
d
x
7
+
6
x
−
x
2
\int \frac{d x}{\sqrt{7+6 x-x^{2}}}
∫
7
+
6
x
−
x
2
d
x
\newline
(
3
3
3
)
∫
d
x
16
−
(
x
−
3
)
2
\int \frac{d x}{\sqrt{16-(x-3)^{2}}}
∫
16
−
(
x
−
3
)
2
d
x
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∫
0
ln
4
20
e
4
x
10
+
e
4
x
d
x
\int_{0}^{\ln 4} \frac{20 e^{4 x}}{\sqrt{10+e^{4 x}}} d x
∫
0
l
n
4
10
+
e
4
x
20
e
4
x
d
x
Get tutor help
∫
1
∞
6
x
+
6
x
2
+
2
x
d
x
\int_{1}^{\infty} \frac{6 x+6}{x^{2}+2 x} d x
∫
1
∞
x
2
+
2
x
6
x
+
6
d
x
Get tutor help
4
4
4
)
\newline
∫
1
5
x
−
1
x
d
x
\int_{1}^{5} \frac{x-1}{x} d x
∫
1
5
x
x
−
1
d
x
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∫
x
2
+
1
(
x
3
+
3
x
−
5
)
3
x
\int \frac{x^{2}+1}{\left(x^{3}+3 x-5\right)^{3}} \mathbb{x}
∫
(
x
3
+
3
x
−
5
)
3
x
2
+
1
x
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lim
x
→
∞
(
x
!
x
x
)
1
/
x
\lim _{x \rightarrow \infty}\left(\frac{x!}{x^{x}}\right)^{1 / x}
lim
x
→
∞
(
x
x
x
!
)
1/
x
Get tutor help
Evaluate
∫
1
x
2
+
6
x
+
13
d
x
\int\frac{1}{x^{2}+6x+13}\,dx
∫
x
2
+
6
x
+
13
1
d
x
\newline
(A)
ln
∣
(
x
+
3
)
2
+
4
∣
+
C
\ln|\left(x+3\right)^{2}+4|+C
ln
∣
(
x
+
3
)
2
+
4∣
+
C
\newline
(B)
−
1
2
tan
−
1
(
x
+
3
2
)
+
C
-\frac{1}{2}\tan^{-1}\left(\frac{x+3}{2}\right)+C
−
2
1
tan
−
1
(
2
x
+
3
)
+
C
\newline
(C)
−
(
1
x
2
+
6
x
+
13
)
−
2
+
C
-\left(\frac{1}{x^{2}+6x+13}\right)^{-2}+C
−
(
x
2
+
6
x
+
13
1
)
−
2
+
C
\newline
(D)
1
2
tan
−
1
(
x
+
3
2
)
+
C
\frac{1}{2}\tan^{-1}\left(\frac{x+3}{2}\right)+C
2
1
tan
−
1
(
2
x
+
3
)
+
C
Get tutor help
254
254
254
. Evaluate
∫
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
(A)
ln
∣
(
x
+
3
)
2
+
4
∣
+
C
\ln \left|(x+3)^{2}+4\right|+C
ln
∣
∣
(
x
+
3
)
2
+
4
∣
∣
+
C
\newline
(B)
−
1
2
tan
−
1
(
x
+
3
2
)
+
C
-\frac{1}{2} \tan ^{-1}\left(\frac{x+3}{2}\right)+C
−
2
1
tan
−
1
(
2
x
+
3
)
+
C
\newline
(C)
−
(
1
x
2
+
6
x
+
13
)
−
2
+
C
-\left(\frac{1}{x^{2}+6 x+13}\right)^{-2}+C
−
(
x
2
+
6
x
+
13
1
)
−
2
+
C
\newline
(D)
1
2
tan
−
1
(
x
+
3
2
)
+
C
\frac{1}{2} \tan ^{-1}\left(\frac{x+3}{2}\right)+C
2
1
tan
−
1
(
2
x
+
3
)
+
C
Get tutor help
1
1
1
.)
∫
0
2
∫
0
1
(
2
y
2
x
2
+
3
)
d
y
d
x
\int_{0}^{2} \int_{0}^{1}\left(2 y^{2} x^{2}+3\right) d y d x
∫
0
2
∫
0
1
(
2
y
2
x
2
+
3
)
d
y
d
x
Get tutor help
x
+
8
x
2
−
6
x
−
7
x
2
+
16
x
+
64
x
+
1
\dfrac{\dfrac{x+8}{x^2-6x-7}}{\,\,\,\dfrac{x^2+16x+64}{x+1}\,\,\,}
x
+
1
x
2
+
16
x
+
64
x
2
−
6
x
−
7
x
+
8
Get tutor help
4
4
4
. Evaluate
lim
x
→
1
x
3
−
1
x
−
1
\lim _{x \rightarrow 1} \frac{x^{3}-1}{x-1}
lim
x
→
1
x
−
1
x
3
−
1
Get tutor help
d
d
x
∫
x
2
3
(
1
2
sin
t
)
d
t
\frac{d}{d x} \int_{x^{2}}^{3}\left(\frac{1}{2} \sin t\right) d t
d
x
d
∫
x
2
3
(
2
1
sin
t
)
d
t
Get tutor help
∫
π
6
π
3
(
1
cos
2
x
−
1
sin
2
x
)
d
x
\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(\frac{1}{\cos ^{2} x}-\frac{1}{\sin ^{2} x}\right) d x
∫
6
π
3
π
(
cos
2
x
1
−
sin
2
x
1
)
d
x
\newline
0
0
0
,
5
5
5
\newline
0
0
0
Get tutor help
∫
0
1
x
d
x
x
4
+
1
=
\int_{0}^{1}\frac{x\,dx}{\sqrt{x^{4}+1}}=
∫
0
1
x
4
+
1
x
d
x
=
Get tutor help
9
9
9
.
∫
0
1
d
x
4
x
2
+
4
x
+
5
\int_{0}^{1} \frac{d x}{4 x^{2}+4 x+5}
∫
0
1
4
x
2
+
4
x
+
5
d
x
.
Get tutor help
∫
x
2
+
2
x
x
−
3
d
x
\int \frac{x^{2}+2 x}{x-3} d x
∫
x
−
3
x
2
+
2
x
d
x
Get tutor help
∫
0
3
∫
0
−
x
+
5
y
2
−
x
d
y
d
x
\int_{0}^{3} \int_{0}^{-x+5} y^{2}-x d y d x
∫
0
3
∫
0
−
x
+
5
y
2
−
x
d
y
d
x
Get tutor help
∫
1
e
−
x
−
1
d
x
\int \frac{1}{e^{-x}-1} d x
∫
e
−
x
−
1
1
d
x
Get tutor help
∫
x
2
d
x
x
2
−
4
\int \frac{x^{2} d x}{x^{2}-4}
∫
x
2
−
4
x
2
d
x
=
Get tutor help
lim
(
x
,
y
)
→
(
0
,
0
)
x
2
+
y
2
x
2
+
y
2
+
1
−
1
\lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}+y^{2}}{\sqrt{x^{2}+y^{2}+1}-1}
lim
(
x
,
y
)
→
(
0
,
0
)
x
2
+
y
2
+
1
−
1
x
2
+
y
2
Get tutor help
If
f
(
x
)
=
(
x
2
+
1
)
3
f(x)=\left(x^{2}+1\right)^{3}
f
(
x
)
=
(
x
2
+
1
)
3
, what is
lim
x
→
−
1
f
(
x
)
−
f
(
−
1
)
x
+
1
?
\lim _{x \rightarrow-1} \frac{f(x)-f(-1)}{x+1} ?
lim
x
→
−
1
x
+
1
f
(
x
)
−
f
(
−
1
)
?
Get tutor help
2
2
2
. Find:
\newline
(a)
∫
13
e
x
d
x
\int 13 e^{x} d x
∫
13
e
x
d
x
\newline
(d)
∫
3
e
−
(
2
x
+
7
)
d
x
\int 3 e^{-(2 x+7)} d x
∫
3
e
−
(
2
x
+
7
)
d
x
\newline
(b)
∫
(
3
e
x
+
4
x
)
d
x
(
x
>
0
)
\int\left(3 e^{x}+\frac{4}{x}\right) d x \quad(x>0)
∫
(
3
e
x
+
x
4
)
d
x
(
x
>
0
)
\newline
(e)
∫
4
x
e
x
2
+
3
d
x
\int 4 x e^{x^{2}+3} d x
∫
4
x
e
x
2
+
3
d
x
\newline
(c)
∫
(
5
e
x
+
3
x
2
)
d
x
(
x
≠
0
)
\int\left(5 e^{x}+\frac{3}{x^{2}}\right) d x \quad(x \neq 0)
∫
(
5
e
x
+
x
2
3
)
d
x
(
x
=
0
)
\newline
(f)
∫
x
e
x
2
!
9
d
x
\int x e^{x^{2}!9} d x
∫
x
e
x
2
!
9
d
x
Get tutor help
Edit
\newline
3
3
3
\newline
Assignment
4
4
4
\newline
1
1
1
. Find the following:
\newline
(a)
∫
16
x
−
3
d
x
(
x
≠
0
)
\int 16 x^{-3} d x \quad(x \neq 0)
∫
16
x
−
3
d
x
(
x
=
0
)
\newline
(d)
∫
2
e
−
2
x
d
x
\int 2 e^{-2 x} d x
∫
2
e
−
2
x
d
x
\newline
(b)
∫
9
x
8
d
x
\int 9 x^{8} d x
∫
9
x
8
d
x
\newline
(e)
∫
4
x
x
2
+
1
d
x
\int \frac{4 x}{x^{2}+1} d x
∫
x
2
+
1
4
x
d
x
\newline
(c)
∫
(
x
5
−
3
x
)
d
x
\int\left(x^{5}-3 x\right) d x
∫
(
x
5
−
3
x
)
d
x
\newline
(f)
∫
(
2
a
x
+
b
)
(
a
x
2
+
b
x
)
7
d
x
\int(2 a x+b)\left(a x^{2}+b x\right)^{7} d x
∫
(
2
a
x
+
b
)
(
a
x
2
+
b
x
)
7
d
x
Get tutor help
24
24
24
.
∫
1
4
(
3
−
∣
x
−
3
∣
)
d
x
\int_{1}^{4}(3-|x-3|) d x
∫
1
4
(
3
−
∣
x
−
3∣
)
d
x
Get tutor help
∫
−
2
1
(
2
−
∣
x
∣
)
d
x
\int_{-2}^{1}(2-|x|) d x
∫
−
2
1
(
2
−
∣
x
∣
)
d
x
Get tutor help
∫
π
4
π
cos
(
2
θ
)
d
θ
\int_{\frac{\pi}{4}}^{\pi} \cos (2 \theta) d \theta
∫
4
π
π
cos
(
2
θ
)
d
θ
Get tutor help
π
4
∫
π
cos
(
2
θ
)
d
θ
\frac{\pi}{4} \int^{\pi} \cos (2 \theta) d \theta
4
π
∫
π
cos
(
2
θ
)
d
θ
Get tutor help
∫
−
π
6
π
3
−
sin
x
cos
2
x
d
x
\int_{-\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{-\sin x}{\cos ^{2} x} d x
∫
−
6
π
3
π
c
o
s
2
x
−
s
i
n
x
d
x
Get tutor help
∫
−
π
6
π
3
−
sin
x
cos
2
x
d
x
\int_{-\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{-\sin x}{\cos ^{2} x} d x
∫
−
6
π
3
π
cos
2
x
−
sin
x
d
x
\newline
Get tutor help
17
17
17
.
\newline
Write the following as a sum of logarithms:
\newline
log
(
x
9
y
2
z
2
)
=
\log \left(x^{9} y^{2} z^{2}\right)=
lo
g
(
x
9
y
2
z
2
)
=
\newline
□
\square
□
log
(
x
)
+
\log (x)+
lo
g
(
x
)
+
□
\square
□
log
(
y
)
+
\log (y)+
lo
g
(
y
)
+
□
\square
□
log
(
z
)
\log (z)
lo
g
(
z
)
\newline
Nextitem
Get tutor help
r
(
x
)
=
∫
−
2
x
2
t
e
4
t
2
d
h
r(x)=\int_{-2}^{x}2te^{4t^{2}}\,dh
r
(
x
)
=
∫
−
2
x
2
t
e
4
t
2
d
h
Get tutor help
∫
0
π
2
x
cos
x
d
x
\int_{0}^{\pi} 2 x \cos x d x
∫
0
π
2
x
cos
x
d
x
Get tutor help
∫
d
x
(
9
+
x
2
)
3
/
2
\int \frac{d x}{\left(9+x^{2}\right)^{3 / 2}}
∫
(
9
+
x
2
)
3/2
d
x
Get tutor help
∫
x
2
d
x
(
x
2
+
16
)
2
\int \frac{x^{2} d x}{\left(x^{2}+16\right)^{2}}
∫
(
x
2
+
16
)
2
x
2
d
x
Get tutor help
∫
−
1
2
x
e
6
x
d
x
\int_{-1}^{2} x e^{6 x} d x
∫
−
1
2
x
e
6
x
d
x
Get tutor help
∫
x
5
x
3
+
1
d
x
\int x^{5} \sqrt{x^{3}+1} d x
∫
x
5
x
3
+
1
d
x
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∫
(
3
x
+
4
)
cos
x
d
x
∫
x
5
x
3
+
1
d
x
\begin{array}{l}\int(3 x+4) \cos x d x \\ \int x^{5} \sqrt{x^{3}+1} d x\end{array}
∫
(
3
x
+
4
)
cos
x
d
x
∫
x
5
x
3
+
1
d
x
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Find the following definite integral.
\newline
∫
−
1
0
2
x
d
x
\int_{-1}^{0} 2 x d x
∫
−
1
0
2
x
d
x
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∫
x
4
+
1
x
2
−
1
d
x
\int \frac{x^{4}+1}{x^{2}-1} d x
∫
x
2
−
1
x
4
+
1
d
x
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∫
x
2
−
1
x
2
x
2
−
1
d
x
\int \frac{\sqrt{x^{2}-1}}{x^{2} \sqrt{x^{2}-1}} d x
∫
x
2
x
2
−
1
x
2
−
1
d
x
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∫
x
2
+
1
x
2
x
2
−
1
d
x
\int \frac{\sqrt{x^{2}+1}}{x^{2} \sqrt{x^{2}-1}} d x
∫
x
2
x
2
−
1
x
2
+
1
d
x
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1
2
3
...
8
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