`int_0^(pi/2)sin^(3)x . sin^(2)x cos^(3)x`

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

int_(0)^(2 pi)sin^(3)x cos^(2)xdx

int_(0)^( pi/2)sin^(3)x*cos^(2)xdx

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

What is int_(0)^(pi//2) (sin^(3)x)/(sin^(3)x + cos^(3)x) dx ?

int_(0)^( pi/2)sin^(2)x cos^(3)xdx

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

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

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

(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