Solving Int. sin(9x)sin(16x)dx w/o Multiple Angles

[ProBasket]

$$\int sin(9x)sin(16x)dx$$

is there another way of solving the problem above besides using the multiple angles formula?

 

[vincentchan]

use this identity:

$$sin u = \frac{e^{iu}-e^{-iu}}{2i}$$

edit:
expand the sine in term of exponential, multiply them and regroup them into 2 cosine, then do the integral

 

[ProBasket]

wow looks more difficult than using multiple angles formula. i just thought there's an easier way to do it so i won't have to remeber crazy amount of formulas when it's test day.

 

[ehild]

$$\int sin(9x)sin(16x)dx$$

is there another way of solving the problem above besides using the multiple angles formula?

use

$$\sin{\alpha}\sin{\beta} = \frac{\cos(\alpha-\beta) - \cos(\alpha + \beta)}{2}$$

ehild

 

[vincentchan]

actually, my way is much much much more easier than remember you formulas...
I can eye ball the answer using my way...
the answer is...
1/14 sin7x - 1/50 sin25x
the expansion of the complex number is easy... there are only 4 terms