e-x-1-e-x-dx-

Question Number 6699 by jose14918645@gmail.com last updated on 14/Jul/16

\int (e^{x} + 1) e^{x} d x

Answered by FilupSmith last updated on 14/Jul/16

= \int e^{2 x} + e^{x} d x

= \frac{1}{2} e^{2 x} + e^{x} + c

Answered by FilupSmith last updated on 15/Jul/16

u = e^{x}

d u = e^{x} d x = u d x

= \int (u + 1) u d x

= \int (u + 1) d u

= \frac{1}{2} u^{2} + u + c

= \frac{1}{2} e^{2 x} + e^{x} + c