   Chapter 7.5, Problem 9E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 2 4 x + 2 x 2 + 3 x − 4 d x

To determine

To evaluate:

24x+2x2+3x-4dx

Explanation

Formula used:

i. dxndx=nxn-1

ii. Integral by parts is also used to solve the integral.

iii. 3.dxx2-a2=12alnx-ax+a

Calculations:

In the given integral ddxx2+3x-4=2x+3

The numerator of the integral can be written as:

x+2=A2x+3+B, such that A=B=1/2

So x+2=122x+3+12

The integral I can thus be written as:

I=12242x+3+1x2+3x-4dx=1224x+3x2+3x-4dx+12241x2+3x-4dx

So I=I1+I2

Note that I1 is in f'f form so it’s integral shall be of ln(f) form. Thus

I1=1224x+3x2+3x-4dx=12lnx2+3x-424=12ln16+12-4-ln4+6-4=12ln24-ln6=12

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