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

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) 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

Evaluate: int_0^(pi//2)1/(4sin^2x+5cos^2x)dx

int_0^(pi/2) (sinx)/(1+Cos^2x)dx

The value of the definite integral int_(0)^((pi)/(2))(sin^(-1)(cos x)+cos^(-1)(cos x))dx is equal to

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

int_0^(pi//2) (sin^(1//2)x)/(sin^(1//2)x+cos^(1//2)x) dx is equal to

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Evaluate: int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx