I need some help to calculate this integral.

$$ \int ^{\frac{\pi}{2}}_{0} \frac{1}{ 3\sin{x}+\cos{x}+15}dx $$

I have no idea how i should act, but I think that in this case the best way is trying with substitution or trying to separate the original integral into two other different pieces.

Any hints to start?


closed as off-topic by Carl Mummert, Davide Giraudo, suomynonA, Daniel W. Farlow, user223391 Nov 2 '16 at 23:58

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Have you tried using the Tangent half-angle substitution?

This simplifies the integrand into

$$ \mathcal{I} = \int_0^1 \frac{\mathrm{d}t}{8+3t+7t^2} $$

Can you finish it from here?

  • $\begingroup$ I think this is definitely what i was looking for. Thank you so much. $\endgroup$ – Gabriele Salvatori Jan 16 '14 at 15:24
  • $\begingroup$ @GabrieleSalvatori. Always think about this method for this kind of integrals. It solves a lot of problems. $\endgroup$ – Claude Leibovici Jan 16 '14 at 15:31

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