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∫
(
x
−
3
e
3
x
)
d
x
\int\left(x-3 e^{3 x}\right) d x
∫
(
x
−
3
e
3
x
)
d
x
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Math Problems
Calculus
Find indefinite integrals using the substitution and by parts
Full solution
Q.
∫
(
x
−
3
e
3
x
)
d
x
\int\left(x-3 e^{3 x}\right) d x
∫
(
x
−
3
e
3
x
)
d
x
Separate into two parts:
Separate the integral into two parts.
\newline
∫
(
x
−
3
e
3
x
)
d
x
=
∫
x
d
x
−
∫
3
e
3
x
d
x
\int(x - 3e^{3x})dx = \int xdx - \int 3e^{3x}dx
∫
(
x
−
3
e
3
x
)
d
x
=
∫
x
d
x
−
∫
3
e
3
x
d
x
Integrate
x
x
x
:
Integrate
∫
x
d
x
\int x\,dx
∫
x
d
x
.
∫
x
d
x
=
1
2
x
2
\int x\,dx = \frac{1}{2}x^2
∫
x
d
x
=
2
1
x
2
Integrate
3
e
3
x
3e^{3x}
3
e
3
x
:
Integrate
∫
3
e
3
x
d
x
\int 3e^{3x}\,dx
∫
3
e
3
x
d
x
. Let
u
=
3
x
u = 3x
u
=
3
x
, then
d
u
d
x
=
3
\frac{du}{dx} = 3
d
x
d
u
=
3
,
d
x
=
d
u
3
dx = \frac{du}{3}
d
x
=
3
d
u
.
∫
3
e
3
x
d
x
=
∫
e
u
d
u
=
e
u
C
\int 3e^{3x}\,dx = \int e^u \,du = \frac{e^u}{C}
∫
3
e
3
x
d
x
=
∫
e
u
d
u
=
C
e
u
, where
C
C
C
is
1
3
\frac{1}{3}
3
1
.
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Evaluate the integral.
\newline
∫
−
3
x
sin
(
−
2
x
)
d
x
\int-3 x \sin (-2 x) d x
∫
−
3
x
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(
−
2
x
)
d
x
\newline
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