2. Evaluate the integral: $$ \int \tan^2 x \sec^6 x \, dx $$
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Since $n$ is an even positive integer, we can save a factor of $\sec^2 x$ and convert the remaining factors of $\sec x$ to $\tan x$ using the identity $\sec^2 x = 1 + \tan^2 x$. Let $u = \tan x$, then $du = \sec^2 x \, dx$. Show more…
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