Mathematics

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


ANSWER

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


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
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