2
$\begingroup$

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?

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Davide Giraudo, suomynonA, Daniel W. Farlow, Community
If this question can be reworded to fit the rules in the help center, please edit the question.

4
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ 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

Not the answer you're looking for? Browse other questions tagged or ask your own question.