Evaluate `int_(oo)^(R) (GMm)/(x^(2))dx`

Evaluate int_(R)^(oo)(GMm)/x^(2)dx

I=int_(-oo)^(1)(1)/(x^(2))dx

Evaluate int_(0)^(oo)((3)/(x^(2)+1))dx

Evaluate int_(0)^(oo)[(3)/(x^(2)+1)]dx where [.] denotes the greatest integer function.

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

int_(3)^(oo)(3)/(x^(2)-1)dx

int_(1)^(oo) (1)/(1+x^(2)) dx =

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta

Evaluate int _(-oo) ^(oo) (1)/(1 + x ^(2)) dx.

Evaluate: int_(0)^(a)(1)/((x^(2)+a^(2)))dx( ii) int_(0)^(oo)(x^(2))/((a^(2)+x^(2))^(5/2))dx