   Chapter 7.4, Problem 41E

Chapter
Section
Textbook Problem

# Make a substitution to express the integrand as a rational function and then evaluate the integral. ∫ d x x 2 + x x

To determine

Make a substitution to express the integrand as a rational function and then evaluate the integral dxx2+xx

Explanation

Calculation: Put x=tx=t2,dx=2tdt

dxx2+xx=2tdtt4+t3=2dtt3+t2=2dtt2(t+1)

Resolve 1t2(t+1) into Partial Fraction

1t2(t+1)=At+Bt2+Ct+1

At(t+1)+B(t+1)+Ct2=1

(A+C)t2+(A+B)t+B=1

Comparing Coefficients of t2,t and t0

A+C=0

A+B=0

B=1

A=1,C=1

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