Find: `intsin^5x dx`

Explanation

Given,

I=`intsin^5x dx`

`I=∫sin^4xsinxdx`

`I=∫(1−cos^2x)^2sinxdx`

Let `u=cosx⇒du=−sinxdx`

`I=−∫(1−u^2)^2du`

`I=−∫(1+u^4−2u^2)du`

`I=−[u+(u^5)/5​−2(u^3)/3​]+c`

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