   Chapter 7.R, Problem 19E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x + 1 9 x 2 + 6 x + 5 d x

To determine

To Find: x+19x2+6x+5dx

Explanation

The above integration can be solved by making denominator in Whole Square and then use the u-substitution.

Calculation:

x+19x2+6x+5=x+19x2+6x+1+4=x+1(3x+1)2+4

The solution of the above integral is given by

x+1 9 x 2 +6x+5 dx= x+1 ( 3x+1 ) 2 +4 dx = 1 3 u1 3 +1 u 2 +4 du [ put3x+1=ux= u1 3 3dx=dudx= du 3 ] = 1 9 u1+3 u 2 +4 du = 1 9 u+2 u 2 +4 du = 1 9 u u 2 +4 du + 2 9 1 u 2 +4

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