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

Evaluate int_(0)^(oo)(dx)/(e^(x)+e^(-x))

int_(0)^(oo)(dx)/((1+x)sqrt(x))

Evaluate :int_(0)^(oo)e^(-x)dx

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

For a>=2, if the value of the definite int_(0)^(oo)(dx)/(a^(2)+(x-((1)/(x)))^(2)) equals (pi)/(5050). Find the value of a.

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

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

int_(0)^(oo)(dx)/((1+x^(2))^(4))=

int_(0)^(oo)(x)/(1+x^(4))dx=

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