Question

Evaluate $\int x{e}^{x}dx$

• A. $e^x(x+1)$
• B. $\frac{e^x}{(x-1)}$
• C. $e^x(x-1)$
• D. $\frac{e^x}{(x+1)}$

Answer 1

The correct option is C $e^x(x-1)$

Using integration by parts we have
$\int x{e}^{x}dx$
$\Rightarrow x\int e^{x}dx-\int (\frac{dx}{dx}\int e^{x}dx)dx$
$\Rightarrow x{e}^x-\int e^{x}dx$
$\Rightarrow x{e}^x-e^x=e^x(x-1)$