Evaluate: `int(x)i spol y nom i a lfu n c t ionoft h en t h degr e e ,p rov et h a t-` `inte^xf(x)dx=e^x[f(x)f^(prime)(x)+f^(x)=f^(x)++(-1)^nf^((n))(x)]` Where `f^((n))(x)d e not e s(d^nf)/(dx^n)`

Explanation

`I=int e^(x)f(x)dx`
`=f(x)e^(x)-int e^(x)f'(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+int e^(x)f''(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+f''(x)e^(x)-inte^(x)f'''(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+f''(x)e^(x)-f'''(x)e^(x)+int e^(x)f'^(v)(x)dx`
continuing this way, we get
`I=e^(x)[f(x)-f'(x)+f''(x)-f'''(x) ...+(-1)^(n)f^((n))(x)]`