`int ((x^2+1)e^x)/(x+1)^2=f(x)e^x`. Find `(d^3f)/(dx^3)` at `x=1`

Evaluate: int((x-1)e^(x))/((x+1)^(3))dx

int(e^(x)+(1)/(x)+2x^(2)+3)dx

int(e^((x)/(2))-1)^(3)e^((x)/(2))dx

If f(x)=e^(x)(x^(2)+1) then find f'(x)

Evaluate int((x-3)e^(x))/((x-1)^(3))dx

int e^(x)((1)/(x^(2))-(2)/(x^(3)))dx

For int (x -1)/( (x +1 ) ^(3)) e ^(x) dx = e ^(x) f (x) + c , f (x) =(x +1) ^(2).

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)/(x^(2)))dx = __________.