integrate x * e ^ x dx = x * e ^ x - k + c

Question

If integrate x * e ^ x dx = x * e ^ x - k + c, find k

Answer 1

\(\int xe^x dx = x \int e^x dx - \int 1.e^x dx + c\)

\(= xe^x - e^x + c\)

\(\therefore k = e^x\)