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I am trying to get the solution of the following symbolic integral using Wolfram-Mathematica:

Integrate[1/(w^2 + l^2 + 2*l*w*Sin[t*w]), w]

but it does not return any solutions. Any ideas how to fix this?

Atd
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  • Thank you. I did try Rubi as you suggested but again it would not return any solutions. – Atd Jan 20 '21 at 13:09

1 Answers1

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When you encounter trigonometric functions (sin, cos), it is often useful to go to the exponential form (see the Help on TrigToExp).

This solves your integral easily:

solutionExp = Integrate[TrigToExp[w^2 + l^2 + 2 l w Sin[t w]], w]

This solution can be brought back to trigonometric form with ExpToTrig:

solutionTrig = ExpToTrig[solutionExp]
ceving
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Bart Romeny
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  • Thank you. If you notice, the expression I wanted to integrate is not the same as what you have tried to solve. The one you offered the solution for is the denominator of the original expression I am interested in. When I try the TrigToExp function on the original expression, it does not work. – Atd Jan 20 '21 at 13:13