Evaluate `int_(-infty)^(infty) 1/(x^2+1)^2dx`

Evaluate int_(0)^(infty) e^(-x)x^(3)dx .

0.) The value of int_(0)^(infty)(a)/(x^(2)+a^(2))dx is : "

A circular coil of N turns carries a current I. Field at a distance x from centre of the loop on its axis is B. Write the value of integral int_(-infty)^(infty) B.dx .

The value of int _(0)^(infty)e-^(a^(2)x^(2)) dx is equal to

Evaluate : int_(-1)^(1)(x^(2))/(1+x^(2))dx

For any ngt1, evaluate the integral int_(0)^(infty)(1)/((x+sqrt(x^(2)+1))^(n))d x

If int_(0) ^(infty ) x^(2)/((x^(2) + a^(2) ) (x^(2) + b^(2)) (x^(2) + c^(2)) )dx = pi/(2(a+b) (b + c) (c+ a)), then int_(0) ^(infty ) dx/((x^(2) + 25) (x^(2) + 36))=