`int a^x/(1+a^(2x))`dx,a>0

int_0^1 x^2 e^(2x) dx

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then

int_0^1 x(1-x)^(5/2) dx

int_(0)^(1)x^2dx

int_(0)^(3)(x^(2)+1)dx

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

The integral int_-a^a (sin^2x)/(1-x^2)dx,0ltalt1 , is equal to (A) int_-a^a (sin^2x)/(1+x^2)dx (B) 2int_0^a (sin^2x)/(1-x^2)dx (C) int_a^0 (sin^2x)/(1+x^2)dx (D) 0

If int_(0)^(1) cot^(-1)(1-x+x^(2))dx=k int_(0)^(1) tan^(-1)x dx , then k=

int_(0)^(oo)((tan^(-1)x)/((1+x^(2))))dx

If I_(1) =int _(0)^(1) (1+x ^(8))/(1+x^(4)) dx sand I_(2)=int _(0)^(1) (1+ x ^(9))/(1+x ^(2)) dx, then: