Question

Solve the integral:$\int x{e}^{x}dx$

Short answer

The required answer is$x{e}^x-e^x+c$.

Step-by-step solution

Step 1. Given information.

We have given integral is$\int x{e}^{x}dx$.

Step 2. Solve the integration by parts .

We have $u=x,dv=e^{x}dx$

The formula of integration by parts is localid="1648636428964" $\int udv=uv-\int vdu$

$$\begin{gathered} \int x{e}^{x}dx \\ =x{e}^x-\int e^{x}dx \\ =x{e}^x-e^x+c \end{gathered}$$