   Chapter 7.5, Problem 68E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x 2 x 6 + 3 x 3 + 2 d x

To determine

To find:

x2x6+3x3+2dx

Explanation

Formula used:1. Integration by partial fractions

Calculations: In the given integral I we simplify the denominator

x6+3x3+2=x6+2x3+x3+2=x3+1x3+2

The integral I can now be written as

I=x2x3+1x3+2dx

In the above equation let x3+2=t, so that, 3x2dx=dt

I can now be written as

I=13dtt(t-1)

Writing 1t(t-1) as partial fraction we have

1t(t-

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