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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!

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  • $\begingroup$ Well, the question gives you a huge hint how to approach the problem: use trigonometric substitution. Have you tried that yet? $\endgroup$ – David H Mar 2 '14 at 7:27
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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?

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