Evaluate: `int_0^(pi//2)(costheta)/((1+sintheta)(2+sintheta))dtheta`

Prove that int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.

Evaluate the following integral: int_0^(pi//2)(sintheta)/(sqrt(1+costheta))d theta

Evaluate: int(1+costheta)/(theta+sintheta)d theta

Evaluate costheta/(1+sintheta)

Evaluate : ( sintheta + costheta ) ( sintheta - costheta )

Prove that int_(0)^(2pi)e^(costheta)cos(sintheta)d theta=2pi .

Iflambda=int_0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)dtheta,t h e n I_1=-2I_2 (b) I_1=I_2 2I_1=I_2 (d) I_1=-I_2

if I=int_(0)^(pi//2)(3sqrt(costheta))/((sqrt(sintheta)+sqrt(costheta))^(5))d theta , then I^(2) is equal to

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

(1-costheta)/(sintheta)+(sintheta)/(1-costheta) =___________.