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Trigonometric Integration

  • #1
∫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]
 
Last edited:

Answers and Replies

  • #2
SammyS
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∫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.
 
  • #3
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
 
  • #4
epenguin
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I think simpler would be just to ask - is there any well known formula involving cosx.sin x ?
 

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