int_(pi/4)^( pi/2)(cos theta)/([cos(theta)/(2)+sin(theta)/(2)]^(3))d theta

int_(pi//4)^(pi//2)(costheta)/((cos\ (theta)/(2)+sin\ (theta)/(2)))\ d theta

Evaluate the following: \int_{(pi)/4}^((pi)/2) frac{cos theta}{[cos (theta/2) + sin (theta/2)]^3} d theta

int_(-pi/2)^(pi/2) cos theta (1+ sin theta)^(2) d theta =

int_(-pi//2)^(pi//2) cos theta (1+sin theta)^(2) d theta=

Show that int_(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2) theta)d theta = (pi)/(6)

Evaluate: \int_{(pi )/4}^(( pi )/2) frac{cos theta }{cos ( theta /2) + sin(theta /2)} d theta

int_(0)^((pi)/(2))(cos theta-sin theta)/((1+cos theta)(1+sin theta))d theta equals -

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =