Chapter 8.5, Problem 32E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding an Indefinite Integral In Exercises 25-32, use substitution and partial fraction to find the indefinite integral. ∫ 1 x ( 3 − x ) d x .

To determine
The solution of the given indefinite integral by using partial fractions.

Explanation

Given:

a. b. c.d. âˆ«e. f.g. 1h. i. x(j.k. l. 3m.n. âˆ’o. xp.q.r. )s.t.u.v. w.dx.x. y.

Formula used:

1. âˆ«1xdx=lnx+C

2. âˆ«dxa2âˆ’x2=12aln|a+xaâˆ’x|+C

Calculation:

Consider the following indefinite integral,

âˆ«1x(3âˆ’x)dx

By rationalising the above function we get,

1x(3âˆ’x)=1(3+x)x(3âˆ’x)(3+x)=3+xx(3âˆ’x)

Simplify further,

3+xx(3âˆ’x)=3x(3âˆ’x)+xx(3âˆ’x)

Use partial fraction method,

3x(3âˆ’x)=Ax+B3âˆ’x3=A(3âˆ’x)+Bx â€¦...â€¦...â€¦...â€¦....

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