Originally Posted by

**ANDS!** Eek, its better to just use LaTex (if you know how) and link the problem.

However this isn't a "simple" integral, unless you are familiar with trig substitutions. Lets do a little bit of math trickery:

$\displaystyle x = 6tan(\theta)$

$\displaystyle dx=6sec^{2}(\theta)d\theta$

Thus:

$\displaystyle \int \frac{6sec^{2}(\theta)d\theta}{(6tan{\theta})^{2}+ 36} \Rightarrow \int \frac6{sec^{2}(\theta)d\theta}{36(tan^{2}\theta+1) }$

From here we simplify:

$\displaystyle \int \frac{sec^{2}(\theta)d\theta}{6sec^{2}(\theta)} \Rightarrow \int \frac{1}{6}d\theta$

This integral is easy to evaluate:

$\displaystyle \int \frac{1}{6}d\theta \Rightarrow \frac{1}{6}\theta+C$

However, we need our final answer in terms of x, not theta. So, we go back to our original substitution:

$\displaystyle x = 6tan(\theta)$

. . .and solve for theta. Do not "memorize" formulas or "tricks" (this really isn't a trick though I called it so) - memorize (or KNOW) identities, and familiar algebraic structures.