List of top Mathematics Questions on Integration by Parts asked in JEE Advanced

If I(m,n) =$\int_0^1 t^m(1+t)n dt ,$ then the expression for I(m, n) in terms of I(m + 1, n - 1) is
The integral $ \int\limits^{1/2}_{-1/2} \bigg ([x] + \log \bigg ( \frac{1+ x}{1 - x} \bigg ) \bigg ) \, dx $ equals