`int_0^(pi//2) cos^3 x*sinx\ dx`

Evaluate the following integral: int_0^(pi//2)1/(5cos x+3sinx)dx

Evaluate : int_0^(pi/2) x sinx dx

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

Evaluate: int_0^(pi/2) cos^2x/(2+sinx+cosx)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

Evaluate: int_0^(pi//2) e^x (sinx-cosx) dx

(i) int_0^(pi/2) sin^2 x dx (ii) int_0^(pi//2) cos^2 x dx

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

int_(0)^((pi)/2)(cos^(3)x)/(sinx+cosx)dx