`inte^(x).[f(x)-f''(x)]dx=`

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)(sin x + cos x)dx =

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

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

The value of int e^(x)[f(x)+f'(x)]dx is equal to -

int e^(x){f(x)-f'(x)}dx=phi(x), then int e^(x)f(x)dx is

Let int e^(x){f(x)-f'(x)}dx=varphi(x) .Then int e^(x)f(x)dx is varphi(x)=

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

Assertion (A) : int e^(x)[sin x - cos x] dx = e^(x) sin x + C Reason (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

Given that int e^x[f(x)+f^'(x)] dx = e^x f(x)+c . Using the given result evaluate int e^x(sinx+cosx)dx