   Chapter 7.5, Problem 47E

Chapter
Section
Textbook Problem

# 7.5 EXERCISESEvaluate the integral. ∫ x 3 ( x − 1 ) − 4 d x

To determine

To find:

x3x-1-4dx

Explanation

Formula used: Integration by partial fractions

Calculations: Simplifying the integrand using partial function we get

fx=x3x-14=Ax-1+Bx-12+Cx-13+Dx-14

x3=A(x-1)3+B(x-1)2+Cx-1+D

x3=Ax3-3x2+3x-1+Bx2-2x+1+Cx-1+D

Equating the RHS and LHS of the above equation we get

A=1

-3A+B=0

3A-2B+C=0

-A+B-C+D=0

On solving these four equations we get

A=1, B=3, C=3, D=1

Putting these values in f(x) we get

fx=1x-1+3x

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