- #1

teneleven

- 12

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## Homework Statement

[tex]\int\frac{dx}{\sqrt{x^2 + 16}}[/tex]

## Homework Equations

[tex]x = 4\tan\theta[/tex]

[tex]dx = 4\sec^2\theta \ d\theta[/tex]

## The Attempt at a Solution

[tex]\int\frac{4\sec^2\theta}{\sqrt{16\tan^2\theta + 16}}\ d\theta[/tex]

[tex]\int\frac{4\sec^2\theta}{\sqrt{16(\tan^2\theta + 1)}}\ d\theta[/tex]

[tex]\int\frac{4\sec^2\theta}{4\sec\theta}\ d\theta[/tex]

[tex]\int\sec\theta\ d\theta[/tex]

How do I reduce past this step?

Integration by parts returns me to [tex]\int\sec\theta\ d\theta[/tex]

The answer at the back of the book is as follows: [tex]\ln(\sqrt{x^2 + 16} + x) + C[/tex]

Thanks.

EDIT: notational mistakes corrected.

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