`int(sin^7 x cos^5 x) dx`

int 1/(sin x cos x) dx

int sin^3x cos^5x dx

(i) int sin^2x cos^3x dx (ii) int sin^3 x cos^2 x dx (iii) int sin^3 x cos^3 x dx

int(sin^3 2x)/(cos^5 2x)dx=

int(sin x)/(cos^(7)x)dx

int(sin x)/(5+cos x)dx

int(sin x)/(1+cos x)dx

int(sin x)/(1-cos 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

Evaluate: (i) int(1)/(sin^(3)x cos^(5)x)dx (ii) int(1)/(sin^(3)x cos x)dx