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Integrate the functionsfprime(a x+b)[f(a...

Integrate the functions`fprime(a x+b)[f(a x+b)]^n`

Text Solution

Verified by Experts

Given `f′(ax+b)[f(ax+b)]^n`
Let `f(ax+b)=t⇒af′(ax+b)dx=dt`
∴`∫f′(ax+b)[f(ax+b)]^ndx=1/a​∫t^ndt`
=`1/a​[t^(n+1)/(n+1)​]`
=`1/(a(n+1))*(f(ax+b))^(n+1)+C`
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