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Find the integral $\int xe^{3x}dx$

Step-by-step Solution

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Solution

Formulas

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Final Answer

$\frac{1}{3}e^{3x}x-\frac{1}{9}e^{3x}+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\int xe^{3x}dx$

Specify the solving method

1

We can solve the integral $\int xe^{3x}dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=x}\\ \displaystyle{du=dx}\end{matrix}$

Learn how to solve integrals of exponential functions problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(xe^(3x))dx. We can solve the integral \int xe^{3x}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

Final Answer

$\frac{1}{3}e^{3x}x-\frac{1}{9}e^{3x}+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(xe^(3x))dx using partial fractionsSolve int(xe^(3x))dx using basic integralsSolve int(xe^(3x))dx using u-substitutionSolve int(xe^(3x))dx using integration by partsSolve int(xe^(3x))dx using tabular integrationSolve int(xe^(3x))dx using trigonometric substitution
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Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

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$\int xe^{3x}dx$

Main topic:

Integrals of Exponential Functions

Used formulas:

5. See formulas

Time to solve it:

~ 0.11 s

Related topics:

Integrals of Exponential FunctionsIntegral CalculusCalculusIntegration by PartsIntegration Techniques

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