Mathematics

# $\displaystyle\int f'(ax+b) [f(ax+b)]^2 dx=$

$\dfrac{[f(ax+b)]^3}{3a}+c$

##### SOLUTION
Now,
$\displaystyle\int f'(ax+b) [f(ax+b)]^2 dx$
$=\dfrac{1}{a}\displaystyle\int f'(ax+b) [f(ax+b)]^2\ adx$
$=\dfrac{1}{a}\displaystyle\int [f(ax+b)]^2 d(f(ax+b))$
$=\dfrac{1}{a}\dfrac{[f(ax+b)]^3}{3}+c$. [ Where  $c$ is integrating constant]

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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