   Chapter 8.2, Problem 8E

Chapter
Section
Textbook Problem

# Using Integration by Parts In Exercises 7–10, evaluate the integral using integration by parts with the given choices of u and dv. ∫ ( 4 x + 7 ) e x d x ,     u = 4 x + 7 ,   d v = e x d x

To determine

To calculate: The value of integral (4x+7)exdx using by-parts.

Explanation

Given:

The provided expression is (4x+7)exdx where, u=4x+7,dv=exdx.

Formula used:

The by-parts rule is udv=uvvdu.

Calculation:

Consider the function (4x+7)exdx. …… (1)

Where u=4x+7,dv=exdx.

Solve both separately.

First,

u=4x+7 …… (2)

Differentiate both sides.

du=4dx …… (3)

Now solve the other one.

dv=exdx …… (4)

Integrate both sides,

v=ex …… (5)

Recall the by-parts rule udv=uvvdu

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