   Chapter 13.6, Problem 1E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 1-32. Identify the formula used. ∫ x 3 x d x

To determine

To calculate: The value of the integral xe3xdx with the help of integral by parts.

Explanation

Given Information:

The provided integral is xe3xdx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

For any variable u, the integral formula is,

enudu=enun+C

Calculation:

Consider the provided integral:

xe3xdx

Now, split the integrand into two parts setting one part equal to u and another part equal to dv.

So, the values will be:

u=x

And,

dv=e3xdx

Then, differentiate u=x on both sides with respect to x,

du=(1)dx

Also, integrate the equation dv=e3xdx by the use of formula enudu=enun+C

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