Q. `int_0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I`

For any value of n in Z , int_(0)^(pi) e^(cos^(2)x) cos^(3) [( 2n +1) x ] dx is

For any integer n , the integral int_0^pie^(cos^2x)cos^3(2n+1)xdx has the value

int_(0)^((pi)/(2)) e^(2x) cos xdx is :

Prove that: int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx = pi^2

int_(0)^(pi/2) (sin x dx)/(1+ cos^2 x ) is

IfI_1=int_0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I_2=int_0^(pi/2)(sin^2x)/(1+sin^2x)dx I_3=int_0^(pi/2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx ,t h e n I_1=I_2> I_3 (b) I_3> I_1=I_2 I_1=I_2=I_3 (d) none of these

Evaluate int_(0)^(pi)(xsinx)/(1+cos^(2)x)dx

Evaluate: int_(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)xdx ,w h e r en in N