   Chapter 7.4, Problem 29E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x + 4 x 2 + 2 x + 5 d x

To determine

To evaluate the integralx+4x2+2x+5dx

Explanation

Calculation: Given x+4x2+2x+5dx

We can write (x2+2x+1)=(x+1)2, so

x+4x2+2x+5dx=(x+1)+3(x+1)2+4dx

Let u=x+1du=dx

Apply the substitution, so

x+4x2+2x+5dx=x+1+3(x+1)2+4dx=u+3u2+4du

Separate the terms, we get

x+4x2+2x+5dx=uu2+4du+3u2+4du

Where, the integrals can be simplified as

=uu2+4du=122uduu2+4=12dzz=12ln|z|

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