   Chapter 8.2, Problem 11E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 11–30, find the indefinite integral. (Note: Solve by the simplest method– not all require integration by parts.) ∫ x e − 4 x d x

To determine

To calculate: The value of integral xe4xdx.

Explanation

Given:

The provided expression is xe4xdx.

Formula used:

The integration formula is udv=uvvdu.

Calculation:

Consider the function xe4xdx. …… (1)

Let, u=x,dv=e4xdx

Solve both separately.

First,

u=x …… (2)

Differentiate both sides.

du=dx …… (3)

Now solve the other one.

dv=e4xdx …… (4)

Integrate both sides,

v=e4x4 …… (5)

Recall the by-parts rule udv=uvvdu.

Substitute values of (u),(du),(v) from equations (2), (3) and (5) respectively in the equation (1)

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