" 3."(f)cos x^(3)*sin^(2)(x^(5))" [NCERT] "(ii)

Evaluate: ( i int(sin^(3)x-cos^(3)x)/(sin^(2)x cos^(2)x)dx (ii) int(5cos^(3)x+6sin^(3)x)/(2sin^(2)x cos^(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(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

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

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

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

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

int ((cos x) ^ (4)) / ((sin x) ^ (3) ((sin x) ^ (5) + (cos x) ^ (5)) ^ ((3) / (5)) ) dx

If f(x)=int_(2x)^(sinx)cos(t^(3))dt then f'(x) is equal to a) cos(sin^(3)x)cosx-2cos(8x^(3)) b) sin(sin^(3)x)sinx-2sin(8x^(3)) c) cos(cos^(3)x)cosx-2cos(x^(3)) d) cos(sin^(3)x)-cos(8x^(3))