求解一道高数定积分!已知f(x)=e^x/x,求∫xf''(x)dx楼下的同学，图在哪

Question

求解一道高数定积分!
已知f(x)=e^x/x,求∫ xf''(x) dx 楼下的同学，图在哪

Answer 1

f(x) = e^x / x
f'(x) = e^x*(x-1) / x²
∫xf''(x) dx
= ∫x df'(x)
= ∫x d[e^x*(x-1) / x²]
= e^x*(x-1) / x - ∫e^x*(x-1) / x² dx
= e^x*(x-1) / x - e^x / x + C
= e^x*(x-2) / x + C