# Indefinite integral

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

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

## Answers and Replies

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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

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wow looks more difficult than using multiple angles formula. i just thought there's an easier way to do it so i wont have to remeber crazy amount of formulas when it's test day.

ehild
Homework Helper
ProBasket said:
$$\int sin(9x)sin(16x)dx$$

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

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