`int_0^((pi)/2) cos^5xsin^4x` dx

Evaluate the following integral: int_0^(pi//4)cos^4xsin^3x\ dx

Evaluate the following integral: int_0^(pi//4)cos^4xsin^3x\ dx

Evaluate int_0^(pi/2) cos ^5 x dx

Evaluate: int_0^(pi/4)cos^2 2xsin^3 4xdx

Evaluate the following integrals int_0^(pi/4)cos^2 2xsin^3 4xdx

(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

int_0^(pi/2) cos^5x/(sin^5x+cos^5x)dx

Prove that int_0^(pi//4) cos^2 2x sin^3 4x dx=1/6

int_0^(pi/4) (cos x- sin x) dx + int_(pi/4)^((5pi)/4) (sinx-cosx) dx + int_(2pi)^(pi/4) (cosx- sinx) dx =