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I'm having a problem resolving the following integral, spent almost all day trying. Any help would be appreciated. $$\int \frac{2\tan(x)+3}{5\sin^2(x)+4}\,dx$$

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    Could you expand on what you've tried?2012-06-07
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    If you expand it like this $\int \frac{2\tan(x)+3}{5\sin^2(x)+4}\,\mathrm{d}x=\int \frac{(2\tan(x)+3)\cos^2 x}{5\sin^2(x)+4}\cdot \frac{\mathrm{d}x}{\cos^2 x}$, the substitution $u=\tan x$ seems reasonable. (You can express both $\sin^2x$ and $\cos^2 x$ using $u=\tan x$).2012-06-07

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