`int_0^oolog(x+1/x)(dx)/(1+x^2)`

int_0^1log(1+x)/(1+x^2)dx

Evaluate: int_0^(1)x(dx)/(sqrt(1-x^(2)))

Evaluate: int_0^(1)x(dx)/(sqrt(1-x^(2)))

If P=int_0^oo(x^2)/(1+x^4)dx ; Q=int_0^oo(x dx)/(1+x^4)"and"R=int_0^oo(dx)/(1+x^4), then prove that :

The value of int_0^oo (dx)/(1+x^4) is (a) same as that of int_0^oo (x^2+1dx)/(1+x) (b) (pi)/(2sqrt2) (c) same as that of int_0^oo (x^2+1dx)/(1+x^4) (d) pi/sqrt2

int_0^1(dx)/(1-x^2)\

int_0^1 int_0^sqrt(1+x^2) (dy dx)/(1+x^2+y^2)

If int_(0)^(1) (e^(x))/( 1+x) dx = k , then int_(0)^(1) (e^(x))/( (1+x)^(2)) dx is equal to

int_0^1 (x/(x+1))dx