What is the integral of xe^{-2x}-3/4 ?

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

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integral of xe^{-2x}-3/4

\int x e^{- 2 x} - \frac{3}{4} d x

\frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) - \frac{3}{4} x + C

Solution steps

\int x e^{- 2 x} - \frac{3}{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x e^{- 2 x} d x - \int \frac{3}{4} d x

\int x e^{- 2 x} d x = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

\int \frac{3}{4} d x = \frac{3}{4} x

= \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) - \frac{3}{4} x

Add a constant to the solution

= \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) - \frac{3}{4} x + C

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