TITLE: Trigonometric Substitution
QUESTION [5 upvotes]: I have been working on some homework problems and there is one problem that has me completely stumped. The question reads: "Evaluate the integral $\int \sqrt{24+4x^2}\,dx$ using trigonometric substitution." I am really unsure how to approach this problem, so if someone could walk me through it I would greatly appreciate it!

REPLY [4 votes]: Recall that $\sec^2\theta=1+\tan^2\theta$. Multiplying this equation by $24$ gives
$$
24\sec^2\theta=24+24\tan^2\theta=24+4\cdot(6\tan^2\theta)
$$
Can you use this equation to find your substitution?