Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

Integrate the function\[\int f'(ax+b)[f(ax+b)]^n\]

Can you answer this question?

1 Answer

0 votes
  • If an integral function $f(x)=t,$ then $f'(x)dx=dt$ then $\int f(x)dx=\int tdt$
  • (ii)$\int x^n dx=\frac{x^{n+1}}{n+1}+c$
Given $I=\int f'(ax+b)[f(ax+b)]^n$
Let $f(ax+b)=t$
On differentiating with respect to x
$f'(ax+b)dx=dt \qquad =>f'(ax+b)dx=\frac{dt}{a}$
Substituting for t and dt
Therefore $I=\frac{1}{a}\int t^n.dt$
On integrating we get
$\frac{1}{a} \bigg[\frac{t^{n+1}}{n+1}+c\bigg]$
Substituting for t we get
$I=\frac{1}{a}[f(ax+b)]^{n+1} \times \frac{1}{n+1}+c$



answered Feb 17, 2013 by meena.p
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App