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

Evaluate the integrals int_(-1)^(1)1(dx)/(x^(2)+2x+5)

Show that (a) int_(e)^(e^(2))(1)/(log x)dx = int_(1)^(2)(e^(x))/(x)dx (b) int_(t)^(1)(dx)/(1+x^(2)) = int_(1)^(1//t)(dx)/(1+x^(2))

"int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

int_(-1)^(1)(dx)/((2-x)sqrt(1-x^(2)))

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

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

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

int_(0)^(1)(dx)/(x^((1)/(2))(1-x)^((1)/(2)))

If int_(0)^(1)(dx)/((1+x)sqrt(1-x^(2)))=(a)/(b) , then