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

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

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 the definite integral int _(0)^(infty) (dx)/((1+x^(a))(1 + x^(2))) (a gt 0) is

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))=

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