`int_0^(pi/2) sin ^4 x (1+ cos x) ^3 dx`

(i) int_0^pi (sin^2 x/2- cos^2 x/2) dx (ii) int_0^(pi//2) (sin^2x)/(1+cosx)^2 dx

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

int_0^(pi/2) sin^4x/(sin^4x+cos^4x) dx=

Compute the integrals I = int_(0)^(pi//4) (sin x + cos x)/( 3 + sin 2 x) dx

int_(0)^(pi) dx/(3+2sin x + cos x) =

int_0^pi sin^4x cos^4x dx

int_0^(pi/2) sin^3x/(sin^3x+cos^3x)dx

Evaluate (i) int_0^(pi//4) sin x cos x dx (ii) int_0^(pi//2) (1 + cos x)^(1//2) dx (iii) int_0^(pi//2) (1 + sin x)^(1//2) dx (iv) int_0^(pi//4) (1 -cos 2x)^(1//2)dx