Hello people

I have been trying for hours to find the reduction formulae for this integrations with futility. Help would be hugely appreciated.

I am at a loss when trying to integrate these expressions by parts. While I decrease the degree of one part, the degree of another part increases so I am held impasse.

I need advise on integration by parts, especially on these types of sums.

Here are the problems:

(a) $\displaystyle \int^1_0 \frac{1}{(1+x^2)^n} dx$

(b) $\displaystyle \int^1_0 x^{n-2} \sqrt(1-x) dx$

The solutions:

(a) $\displaystyle 2(n-1)I_n=2^{1-n} + (2n-3) I_{n-1}$

(b) $\displaystyle I_n=\frac{n}{n+3} I_{n-2}$

Please help me