# Math Help - Reduction formula problem..

1. ## Reduction formula problem..

Can someone help me with this question..

For the integral $\int{\frac{1}{( x^2 + 1 )^n}} dx$ prove the reduction formula :
$I_{n} = \frac{1}{n-2} . \frac{x}{(x^2+1)^{n-1}} + \frac{2n - 3}{2n-2}I_{n-1}$

Thanks

2. ## Re: Reduction formula problem..

How to find the integral of
a) $\int{\frac{3}{\sqrt{6 + 4x - x^2}}}$

and

b) $\int{\frac{3x^2}{\sqrt{x^2 - 9}}}$

for b) The answer in the ans sheet is this

$\frac{3x \sqrt{x^2 - 9}}{2} + \frac{27}{2} ln (x + \sqrt{x^2 -9}) + C$

What I've found is this :

$\frac{27}{3} ln (\frac{1}{3} + \sqrt{x^2 -9})$

and

c) $\int{x^3 ln (ax)}$

Ans : $-\frac{x^4}{10}+ \frac{x^4 ln (ax)}{4}$

My ans : $-\frac{x^4}{16}+ \frac{x^4 ln (ax)}{4}$