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# more Calc II homework...?

integrate:

sin(7x) cos(5x) +C

I got...

-1/24 cos (12x) - 1/4 cos (2x) + C

Is it correct?

Thanks :)

that's the answer wolfram mathematica gave as well but I'm not sure how to get the 1/2 cos(x).... can you show work??

### 1 Answer

- Ed ILv 71 decade agoFavorite Answer
sin 7x cos 5x = (1/2) [ sin (7x + 5x) + sin (7x - 5x) = (1/2) (sin 12x + sin 2x)

Integrating, (1/2) ∫ (sin 12x + sin 2x) dx = (1/2) [(-1/12) cos 12x - (1/2) cos 2x] = (-1/24) cos 12x - (1/4) cos 2x + C

Honestly, if you hadn't shown your answer, I probably would have tried to integrate the original expression, using some trig substitution, but your way is easier.