Theorem: `d/dx(int f(x) dx) = f(x)`

int[(d)/(dx)f(x)]dx=

Statement-1: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^x Statement-2: d/dx(f(x))^(g(x))=(f(x))^(g(x))d/dx[g(x)logf(x)] (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Let f(t)="ln"(t) . Then, (d)/(dx)(int_(x^(2))^(x^(3))f(t)" dt")

int_a^b[d/dx(f(x))]dx

int(ax+b)/(cx+d)dx