" 9.(i) "(1)/(sin x cos^(3)x)

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

3. (sin x+cos x)(1-sin x cos x)=sin^(3)x+cos^(3)x

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) 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

The value of x satisfying the equation (sin^(-1)x)^(3)-(cos^(-1)x)^(3)+(sin^(-1)x)(cos^(-1)x)(sin^(-1)x-cos^(-1)x)=(pi^(3))/(16) is :

9Prove that the values of the function (sin x cos3x)/(sin3x cos x) cannot lie between (1)/(3) and 3 for any real x

The value of (2(sin2x+2cos^(2)x-1))/(cos x sin x cos3x+sin3x) is

Evaluate: (i) int(1+cos x)/((x+sin x)^(3))dx (ii) int(cos x-sin x)/(1+sin2x)dx