`1f I=int(dx)/((2a x+x^2)^(3/2))`

Let f(x)=int(1)/((1+x^(2))^(3//2))dx and f(0)=0 then f(1)=

Consider the integral I=int(xe^(x))/((1+x)^(2))dx What is the value of inte^(x)(f(x)+f'(x))dx ?

If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(0)=0, then the value of |2/(f(2))| is___

Evaluate : (i) int(2x)/((2x+1)^(2))dx (ii) int((2+3x))/((3-2x))dx

If f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx and f(0)=0, then the value of (2)/(f(2))| is

If I_(1) int sin^(-1) ((2x)/(1 +x^(2)) ) dx , I_(2) = int cos^(-1) ((1-x^(2))/(1 +x^(2)) ) dx , I_(3) = int tan^(-1) ((2x)/(1 - x^(2)) ) dx , then I_(1) + I_(2) - I_(3) =