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

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

int_(0)^(oo)(x)/((1+x)(1+x^(2))) dx equals to :

The value of definite integral int _(0)^(oo) (dx )/((1+ x^(9)) (1+ x^(2))) equal to:

The value fo the integral I=int_(0)^(oo)(dx)/((1+x^(2020))(1+x^(2))) is equal to kpi , then the value of 16k is equal to

Prove that: int_(0)^(oo) (x)/((1+x)(1+x^(2)))dx =(pi)/(4)

If I_(1)=int_(0)^(oo) (dx)/(1+x^(4))dx and I_(2)=underset(0)overset(oo)int x^(2)(dx)/(1+x^(4))"then"n (I_(1))/(I_(2))=

Let I_(1)=int_(0)^(oo)(x^(2)sqrtx)/((1+x)^(6))dx,I_(2)=int_(0)^(oo)(xsqrtx)/((1+x)^(6))dx , then

The value of int_(0)^(oo) (logx)/(1+x^(2))dx , is

The value of int_(0)^(oo)(logx)/(a^(2)+x^(2))dx is

The value of int_(0)^(oo)(dx)/(1+x^(4)) is equal to