" 32."int e^(x)[f(x)+f'(x)]dx=

inte^(x)[f(x)+f'(x)]dx=

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

int e^(ax)[a f(x)+f' (x)]dx=

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

int e^x[f(x)+f^1(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)((x-1)/(x^(2)))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(x e^(x))/((1+x)^(2))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)(x+1)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