Is there a known formula for integrating cos^5x sin^5x?

[johnhuntsman]

∫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.

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

 

[SammyS]

∫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.

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

How did you get it?

Take the derivative, to check it.


Don't forget the constant of integration.

 

[johnhuntsman]

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]

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