integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

An image showing the results of your requested integral.


Integrate[E^(a*x)*Sin[b*x]*Sin[c*x], x] ==
(E^(a*x)*((a*Cos[(b - c)*x] + (b - c)*Sin[(b - c)*x])/ (a^2 + (b - c)^2) - (a*Cos[(b + c)*x] + (b + c)*Sin[(b + c)*x])/(a^2 + (b + c)^2)))/2



           a x
Integrate[E    Sin[b x] Sin[c x], x] == 

  a x  a Cos[(b - c) x] + (b - c) Sin[(b - c) x]
(E    (----------------------------------------- - 
                      2          2
                     a  + (b - c)
 
      a Cos[(b + c) x] + (b + c) Sin[(b + c) x]
      -----------------------------------------)) / 2
                     2          2
                    a  + (b + c)

Time to compute: 0.67 second

Spread the word: