What is the integral of xe^{-2}+ex^{-2} ?

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

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integral of xe^{-2}+ex^{-2}

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

\frac{x ^{2}}{2 e ^{2}} - \frac{e}{x} + C

Solution steps

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

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

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

= \frac{x ^{2}}{2 e ^{2}} - \frac{e}{x}

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{2}} - \frac{e}{x} + C

\frac{\partial}{\partial z} (x y^{2} z^{3})

arctan (\frac{x - 1}{x + 1})

\int \frac{e ^{3 x}}{1 - 2 e ^{3 x}} d x

ln (sin (x))

y^{^{'}} = y x^{2}

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