[" (N.C.E "],[" (ii) "(2-3sin x)/(cos^(2)x)]

int(cos x)/(cos((x)/(2))+sin((x)/(2)))^(5)dx=,[[" (A) "(2)/(3)(cosec((x)/(2))+sec((x)/(2)))^(3)+c," (B) "(2)/(3)(cos((x)/(2))+sin((x)/(2)))^(3)+c],[" (C) "(2)/(3)(sin((x)/(2))-cos((x)/(2)))^(-3)+c," (D) "-(2)/(3)(sin((x)/(2))+cos((x)/(2)))^(-3)+c]]

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))=

(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

Evaluate: (i) int(e^(2x))/(e^(2x)-2)dx (ii) int(2cos x-3sin x)/(6cos x+4sin x)dx

int (e ^ (sin x)) / (cos ^ (2) x) (x cos ^ (3) x-sin x) dx

Evaluate: (i) int(sin2x)/(a cos^(2)x+b sin^(2)x)dx (ii) int(cos x)/(2+3sin x)dx

int(e^(x)+2sin x-3cos x)dx

If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= (a) -y/x (b) (3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y)) (c) (3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y)) (d) (sin^2(a+y))/(sina)