   Chapter 7.4, Problem 43E

Chapter
Section
Textbook Problem

# Make a substitution to express the integrand as a rational function and then evaluate the integral. ∫ x 3 x 2 + 1 3 d x

To determine

Make a substitution to express the integrand as a rational function and then evaluate the integral x3x2+13dx

Explanation

Calculation: Put x2+1=t32xdx=3t2dtxdx=32t2dt

x3dx=x2(xdx)=(t31).32t2dt=32t2(t31)dt

x3x2+13dx=32t2(t31)tdt=32t(t31)dt

=32

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