f'(ax+b)[f(ax+b)]ⁿ - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.

Question : 245 of 271

Marks: +1, -0

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

Solution:

Let

I=\int f'(ax+b)[f(ax+b)]^n\,dx

Let

f(ax+b)=t

\Rightarrow af'(ax+b)dx=dt

\therefore I=\frac{1}{a}\int t^n\,dt=\frac{1}{a}\cdot\frac{t^{n+1}}{n+1}+C

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

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