" (c) "f(x)=e^(x)

PARAGRAPH : If function f,g are continuous in a closed interval [a,b] and differentiable in the open interval (a,b) then there exists a number c in (a,b) such that [g(b)-g(a)]f'(c)=[f(b)-f(a)]g'(c) If f(x)=e^(x) and g(x)=e^(-x) , a<=x<=b c=

The function f:R rarr R defined by f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)) is

Observe the following statements A : int (((x^(2)-1)/(x^(2))).e^((x^(2)+1/x)) dx = e^((x^(2)+1)/x) + c R: int f^(')(x).e^(f(x)) dx = f(x) + c Then which of the following is true?

A: int e^(x)((1+x log x)/(x))=e^(x)log x+c R: int e^(x)[f(x)+f'(x)]dx=e^(x)f(x)+c

Evaluate: int e^(x)(f(x)+f'(x))dx=e^(x)f(x)+C

Statement-I: int e^(x) sinxdx=(e^(x))/(2)(sinx-cosx)+c Statement-II: int e^(x)(f(x)+f'(x))dx=e^(x)f(x)+c

Statement 1: int(xe^(x)dx)/((1+x)^(2))=(e^(x))/(x+1)+C Statement 2: inte^(x)(f(x)+f'(x))dx=e^(x)f(x)+C

Show that int e^(x)[f(x)+f'(x)]dx=e^(x).f(x)+c Hence, evaluate: int e^(x)((2+sin2x)/(1+cos2x))dx

f: R to R is a function defined by f(x) =(e^(|x|) -e^(-x))/(e^(x) + e^(-x)) . Then f is: