   Chapter 12.3, Problem 32E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 1-32. ∫ x 4 − 2 x 2 + x x 2 − 2 d x

To determine

To calculate: The value of the integral x42x2+xx22dx.

Explanation

Given Information:

The provided integral is:

x42x2+xx22dx

Formula used:

According to the power rule of integrals:

xndx=xn+1n+1+C

If u is a function of x,

u1udx=uudx=1udu=ln|u|+C

Calculation:

Consider the provided integral,

x42x2+xx22dx

Simplify the integral algebraically as,

x42x2+xx22dx=x2(x22)+xx22dx=(x2+xx22)dx=(x2)dx+122xx22dx

Now, use the power rule and the integral formula,

u1udx=

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