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Integrate (cosx)(sinx)^3

I've tried splitting it up into (cosx)(sinx)(sinx)^2, and then using various identities, but that's really long-winded. The shortness of the other questions in the exercise leads me to believe that there is a better way?

HALP :frown:
Reply 1
Avatar for Skadoosh
Skadoosh
12
Substitution perhaps?
Reply 2
Avatar for maxfire
maxfire
14
u=sinx
Reply 3
Avatar for nicknick
nicknick
cos x is the derivative of sin x, so this is simply a reverse chain rule job, surely?
Reply 4
Avatar for Jingers
Jingers
15
Because sinx differentiates to cosx, you just integrate (sinx)^3 to get ((sinx)^4)/4
Reply 5
Avatar for Tallon
Tallon
16
It's not that long-winded is it?
but yeah, just do a simple substitution.

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