# Trigonometric Integration

∫cos^5 x sin^5 x dx

I thought I would try to solve this by first doing:

∫(1 - sin^2 x) cos^3 x sin^5 x dx

but would like to know if that's right.

 Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?

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SammyS
Staff Emeritus
Homework Helper
Gold Member
∫cos^5 x sin^5 x dx

I thought I would try to solve this by first doing:

∫(1 - sin^2 x) cos^3 x sin^5 x dx

but would like to know if that's right.

 Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?
How did you get it?

Take the derivative, to check it.

Don't forget the constant of integration.

How did you get it?
I split up the cos^3 x just like I did the cos before. Then used u substitution.

Take the derivative, to check it.
I did. Thanks, everything's okey dokey now : D

epenguin
Homework Helper
Gold Member
I think simpler would be just to ask - is there any well known formula involving cosx.sin x ?