   Chapter 6.1, Problem 34E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Finding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) ∫ x x + 2 3   d x

To determine

To calculate: The value of indefinite integral xx+23dx.

Explanation

Given Information:

The provided indefinite integral is xx+23dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

(ax+b)ndx=1a(ax+b)n+1n+1,n1

Calculation:

Consider the indefinite integral xx+23dx

Here,

dv=(x+2)13dx and u=x

First find v,

dv=(x+2)13dxdv=(x+2)13dx

On further solving,

v=34(x+2)13 …...…... (1)

Now find du,

u=x

Differentiate both side with respect x,

dudx=d(x)dxdudx=1

And,

du=1dx …...…... (2)

Apply integration by parts formula and substitute equation (1) and (2) in udv=uvvdu,

xx+23dx=34x(x+2)4334(x+2)43dx

Apply the formula (ax+b)ndx=1a(ax+b)n+1n+1,n1,

xx+23dx=34x(x+2)43928(x+2)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### let f(x) = x3 + 5, g(x) = x2 2, and h(x) = 2x + 4. Find the rule for each function. 7. fgh

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: If the three limits exist, then .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### The area of the region bounded by , , and r = sec θ is:

Study Guide for Stewart's Multivariable Calculus, 8th 