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

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

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integral of e^{1/2}x^2

integral

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

\frac{e ^{\frac{1}{2}} x ^{3}}{3} + C

Solution steps

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

Apply the Power Rule

= e^{\frac{1}{2}} \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{e ^{\frac{1}{2}} x ^{3}}{3}

Add a constant to the solution

= \frac{e ^{\frac{1}{2}} x ^{3}}{3} + C

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