What is the integral of esqrt(x) ?

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

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integral of esqrt(x)

\int e x d x

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

Solution steps

\int e x d x

Take the constant out:

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

= e \cdot \int x d x

Apply the Power Rule

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

Add a constant to the solution

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