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

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

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integral of (2xe^{-x^2})e^{x^2}

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

x^{2} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Simplify

x e^{- x^{2}} e^{x^{2}} : x

= 2 \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 2 \cdot \frac{x ^{2}}{2}

Simplify

2 \cdot \frac{x ^{2}}{2} : x^{2}

= x^{2}

Add a constant to the solution

= x^{2} + C

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