Solution
= Solution
Here $I_0=x$ up to a constant. Substitution of $n=0$ in the <integration by parts> recurrence gives
$$
\boxed{I_1=x\ln x-x+C},\qquad x>0.
$$
Indeed, its <derivative> is $\ln x+1-1=\ln x$.
= Solution
Here $I_0=x$ up to a constant. Substitution of $n=0$ in the <integration by parts> recurrence gives
$$
\boxed{I_1=x\ln x-x+C},\qquad x>0.
$$
Indeed, its <derivative> is $\ln x+1-1=\ln x$.