   Chapter 7.R, Problem 52E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0 ). ∫ x 3 x 2 + 1 d x

To determine

To Find:x3x2+1dx

Explanation

Initially looking at the integrand, you don’t have any clue how to integrate. But if you look the integrand carefully, we can use substitution method. Let x2+1=t2 and differentiate it to get

2xdx=2tdt

Now,

x3x2+1dx=x2×xdxx2+1=(t21)×tdtt=(t21)dt=13t3t

Substitute x=t21 to the integral in original variable x

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