`int_0^pi(x dx)/(1+cos^2x)=(pi^2)/(2sqrt(2))`

int_0^pi (xSinx)/(1+Cos^2x)dx

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

Find the mistake of the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]pi0=0

Find the mistake in the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) , then : I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]_pi^0=0

Find the mistake in the following evaluation of the integral I=int_0^pi(dx)/(1+2sin^2x) , then : I=int_0^pi(dx)/(cos^2x+3sin^2x) =int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]_pi^0=0

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

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^(pi/2) (sinx)/(1+Cos^2x)dx

int_0^pi (cos^2x)dx ,

Prove that int_(0)^(pi)(xsin^(3)x)/(1+cos^(2)x)dx=pi/2(pi-2)