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

The integral of (y+1)e^{-2y} is -1/2 e^{-2y}y-3/4 e^{-2y}+C

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

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

- \frac{1}{2} e^{- 2 y} y - \frac{3}{4} e^{- 2 y} + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{2} e^{- 2 y} d y = \frac{1}{4} e^{- 2 y}

= - \frac{1}{2} e^{- 2 y} (y + 1) - \frac{1}{4} e^{- 2 y}

Simplify

- \frac{1}{2} e^{- 2 y} (y + 1) - \frac{1}{4} e^{- 2 y} : - \frac{1}{2} e^{- 2 y} y - \frac{3}{4} e^{- 2 y}

= - \frac{1}{2} e^{- 2 y} y - \frac{3}{4} e^{- 2 y}

Add a constant to the solution

= - \frac{1}{2} e^{- 2 y} y - \frac{3}{4} e^{- 2 y} + C

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4)^{2})

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\frac{d}{d x} (10, 0 - 40 x - 0.02 x^{2})

x \to c lim (x^{2} + a)

What is the integral of (y+1)e^{-2y} ?
The integral of (y+1)e^{-2y} is -1/2 e^{-2y}y-3/4 e^{-2y}+C