   Chapter 13, Problem 5T ### 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

# Use integration by parts to evaluate the following. ∫ 3 x e x d x ∫ x ln ( 2 x ) d x

(a)

To determine

To calculate: The value of the integral 3xexdx.

Explanation

Given Information:

The provided integral is 3xexdx.

Formula used:

The formula for integration by parts is udv=uvvdu.

The exponential rule of integral is exdx=ex+C.

Calculation:

Consider the integral, 3xexdx

Now, split the integrand into two parts,

So, u=3x and dv=exdx

Then,

du=3dx

And,

v=exdx=ex+C

Use the formula for integration by parts,

u

(b)

To determine

To calculate: The value of the integral xln(2x)dx.

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