- #1

- 559

- 8

## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

[tex]x=4tan\theta[/tex] [tex]dx=4sec^{2}\theta d\theta[/tex]

Therefore:

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

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

[tex]=ln|sec\theta+tan\theta| = ln|sec\frac{\sqrt{x^{2}+16}}{4}+tan\frac{x}{4}|[/tex]

Wolfram is getting a hyperbolic sine function so idk what is wrong (we've never talked about hyperbolic functions in class, so I don't think that's the answer)