int(f'(x))/([f(x)]^(2))dx=

The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-x))dx is equal to

The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-x))dx is equal to

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int(x e^(x))/((1+x)^(2))dx = ________.

Match the following {:("List - I "," List II "),( (A) int (f^(1)(x))/(f(x)) dx = ,(1) 2 sqrt(f(x)) +c ),((B) int (f^(1)(x))/(sqrt(f(x))) dx= , (2) (2)/(3) (f(x))^(3//2) + c ),((C) int f^(1) (x) sqrt(f(x)) dx =, (3)" log | f(x)| + c"),((D) int f^(1) (x).(f(x))^(2) dx = , (4) (1)/(3) (f(x))^(3) + c ):} The correct match for list -I from List - II is

int2^(x)(f'(x)+f(x)log2)dx is equal to

int 2^x(f'(x)+f(x)log2)dx is equal to:

int2^x(f'(x)+f(x)log2)dx is equal to

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)((x-1)/(x^(2)))dx = __________.

If int f(x)dx = F(x), f(x) is a continuous function,then int (f(x))/(F(x))dx equals