# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

$\int\:xe^{3x}\:dx$

Solving method

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

$u=e^{3x}$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x*2.718281828459045^(3*x))dx. We can solve the integral \int xe^{3x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that e^{3x} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Rewriting x in terms of u.

$\frac{1}{3}e^{3x}x-\frac{1}{9}e^{3x}+C_0$
$\int\:xe^{3x}\:dx$