Question

The value of $\int (x-1)e^{-x}$ dx is equal to

• A. $-x{e}^x+C$
• B. $x{e}^x+C$
• C. $-x{e}^{-x}+C$
• D. $x{e}^{-x}+C$

Answer 1

Answer: (A), (C)

$-x{e}^x+C$
$-x{e}^{-x}+C$

$I=\int (x-1)e^{-x}$

$=\int x{e}^{-x}dx-\int e^{-x}dx$

$=-x{e}^{-x}-\int 1.(-)e^{-x}dx-\int e^{-x}dx+c$

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

$=-x{e}^{-x}+c$