" 14.(i) "4sin x^(2)+log(5sin x+c)

x^(2)log sin x

log(sin x^2)

(i) int tan dx=log |secx|+c (ii) int cot x dx=log |sin x|+c (iii) int tan x dx=log |sin x| +c (iv) int tan x dx =-log cos x +c

int(9cos x-sin x)/(4sin x+5cos x)dx=A log|4sin x+ 5cos x| + Bx + c , then A=...,B=..

Evaluate: (i) int(sin2x)/(sin5x sin3x)dx (ii) int(1+cot x)/(x+log sin x)dx

If y={(log)cos x sin x}{(log)_(sin x)cos x}^(-1)+sin^(-1)((2x)/(1+x^(2))) fin d (dy)/(dx)atx=(pi)/(4)

The value of the integral int(cos^(3)x+cos^(5)x)/(sin^(2)x+sin^(4)x)dx is (A) sin x-6tan^(-1)(sin x)+C(B)sin x-2(sin x)^(-1)+C(C)sin x-2(sin x)^(-1)+6tan^(-1)(sin x)+C(D)sin x-2(sin x)^(-1)+5tan^(-1)(sin x)+C

int_(sqrt(ln2))^(sqrt(ln3))(x sin x^(2))/(sin x^(2)+sin(ln6-x^(2)))dx is