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  • Integrate the functions in Exercises 1 to 24. f'(ax + b)[f(ax + b]^n

Integrate the functions in Exercises 1 to 24.

    Q17.    f'(ax +b)[f(ax +b)]^n

Answers (1)

best_answer

Given,

f'(ax +b)[f(ax +b)]^n

Let  I = \int f'(ax +b)[f(ax +b)]^n

Let f(ax +b) = t ⇒ a .f ' (ax + b)dx = dt

Now we can write the integral as

\int f'(ax +b)[f(ax +b)]^n = \frac{1}{a}\int t^ndt

\\ = \frac{1}{a}.\frac{t^{n+1}}{n+1} + C \\ = \frac{1}{a}.\frac{(f(ax+b))^{n+1}}{n+1} + C

\implies I = \frac{(f(ax+b))^{n+1}}{a(n+1)} + C

Posted by

HARSH KANKARIA

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