# Homework Help: Tricky integral

1. Jul 12, 2011

### cal.queen92

1. The problem statement, all variables and given/known data

indefinite integral: dx/(x*sqrt(9+16x^2))

2. Relevant equations

Trig. Substitutions or parts??

3. The attempt at a solution

I tried using integration by parts but its got pretty messy....it also resembles a tan trig substitution, but it's within a square root. I'm stumped and can't figure out where to start....

Can anyone help?

Thanks!

2. Jul 12, 2011

### HallsofIvy

Don't use integration by parts. Rewrite the problem as
$$\int\frac{xdx}{x^2\sqrt{9+ 16x^2}}$$
and let $u= 9+ 16x^2$.

Last edited by a moderator: Jul 13, 2011
3. Jul 12, 2011

### SammyS

Staff Emeritus
Factor a 3 out of $\sqrt{9 +16x^2}$

$$\displaystyle \sqrt{9 +16x^2}=\sqrt{9\left(1+\frac{16x^2}{9}\right)}=3 \sqrt{1+\frac{16x^2}{9}}=3 \sqrt{1+\left( \frac{4x}{3} \right)^2 }$$

We know that 1+tan2(θ) = sec2(θ) , so let 4x/3 = tan(θ), (4/3)dx = sec2(θ)dθ.

(I'm slow at typing, so HallsofIvy responded while I was typing. He usually has better ideas than I do. Good luck!)

Last edited: Jul 12, 2011
4. Jul 12, 2011