   Chapter 12.3, Problem 30E ### 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. ∫ 2 x 3 + x 2 + 2 x + 3 2 x + 1 d x

To determine

To calculate: The value of the integral 2x3+x2+2x+32x+1dx.

Explanation

Given Information:

The provided integral is:

2x3+x2+2x+32x+1dx

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,

2x3+x2+2x+32x+1dx

Perform the long division of integrand as,

2x+1x2+12x3+x2+2x+32x3+x2            _                 2x+3                 2x+1_                         2

So the integral can be written as,

2x3+x2+2x+32x+1=x2+1+22x+1

Rewrite the provided integral as,

2x3+x2+2x+32x+1dx=(x2+1)dx+212x+1dx</

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