Evaluate: `int_(-pi)^(3pi)log(s e ctheta-t a ntheta)dtheta`

Evaluate: int_(-pi/2)^(pi/2)log((a-s intheta)/(a+sintheta))dtheta,a >0

Evaluate int_((-pi)/2)^(pi/2)cosxdx .

Evaluate: int_(-pi//2)^(pi//2)xsin dx

Evaluate : int_((-pi)/2)^(pi/2)xcosxdx .

If f(x) is an integrable function for x in [pi/6,pi/3]a n d I_1=int_(pi/6)^(pi/3)sec^2thetaf(2sin2theta)dtheta,a n d I_2=int_(pi/6)^(pi/3)"c o s e c"^2thetaf(2sin2theta)dtheta,t h e n(I_1)/(I_2)=

Evaluate: int_(pi//4)^(pi//4)log(sinx+cosx)dx

Evaluate: int_(-pi)^pi(xsinx dx)/(e^x+1)

Evaluate int_(0)^(pi)xsin^(3)xdx

If int_0^(pi/2)logsinthetadtheta=k , then find the value of int_pi^(pi/2)(theta/(s intheta))^2dtheta in terms of k

Evaluate int_(0)^(pi//6) cos^(7) 3x dx