   Chapter 7.6, Problem 42E

Chapter
Section
Textbook Problem

# Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. ∫ x 2 1 − x 2 d x

To determine

To Find: The value of the integral x21x2dx

Explanation

Calculations: Given x21x2dx

From the Table of Integrals, we use Entry No 31

u2a2u2du=u8(2u2a2)a2u2+a48sin1(ua)+C

Therefore

x21x2dx=x8(2x21)1x2+18sin1(x)+C

The value of the integral obtained using CAS (https://www.integral-calculator.com/) is

x21x2dx=18arcsinxx4(1x2)32+x81x2+C

We may simplify the above equation and show that it is indeed same as computed answer

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