What is the integral of (1+2x)e^{-x} ?

The integral of (1+2x)e^{-x} is -2e^{-x}x-3e^{-x}+C

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integral of (1+2x)e^{-x}

\int (1 + 2 x) e^{- x} d x

- 2 e^{- x} x - 3 e^{- x} + C

Solution steps

\int (1 + 2 x) e^{- x} d x

Apply Integration By Parts

: - e^{- x} (1 + 2 x) - \int - 2 e^{- x} d x

= - e^{- x} (1 + 2 x) - \int - 2 e^{- x} d x

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

= - e^{- x} (1 + 2 x) - 2 e^{- x}

Simplify

- e^{- x} (1 + 2 x) - 2 e^{- x} : - 2 e^{- x} x - 3 e^{- x}

= - 2 e^{- x} x - 3 e^{- x}

Add a constant to the solution

= - 2 e^{- x} x - 3 e^{- x} + C

\int \frac{x ^{2}}{x ^{2} - 6 x + 25} d x

x \to - \infty lim (e^{4 x})

\int_{4}^{8} \frac{x}{x ^{2} + 4 x + 20} d x

\frac{\partial}{\partial x} (x^{x})

x \to \infty lim (9.35 e^{(- 0.4 x)} + 5.52)

What is the integral of (1+2x)e^{-x} ?
The integral of (1+2x)e^{-x} is -2e^{-x}x-3e^{-x}+C