What is the integral of xe^{1/2} ?

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

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integral of xe^{1/2}

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

\frac{e ^{\frac{1}{2}} x ^{2}}{2} + C

Solution steps

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

Take the constant out:

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

= e^{\frac{1}{2}} \cdot \int x d x

Apply the Power Rule

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

= e^{\frac{1}{2}} \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{\frac{1}{2}} x ^{2}}{2}

Add a constant to the solution

= \frac{e ^{\frac{1}{2}} x ^{2}}{2} + C

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