   Chapter 8.4, Problem 28E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 19-32, find the indefinite integral. ∫ 1 x 9 x 2 + 1   d x

To determine

To calculate: The solution of indefinite integral 1x9x2+1dx.

Explanation

Given:

The indefinite integral, 1x9x2+1dx.

Formula used:

The integral formula, cosecθdθ=ln|cosecθ+cotθ|+C

Calculation:

Because 9x2+1 is of the form a2+x2, make use of the trigonometric solution, 3x=tanθ to solve it.

The derivative of the above equation is;

3dx=sec2θdθ

Therefore,

1x9x2+1dx=3tanθtan2θ+1sec2θ3dθ=sec2θsecθtanθdθ=secθtanθdθ=<

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