What is the integral of 3/2 sqrt(x) ?

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

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integral of 3/2 sqrt(x)

\int \frac{3}{2} x d x

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

Solution steps

\int \frac{3}{2} x d x

Take the constant out:

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

= \frac{3}{2} \cdot \int x d x

Apply the Power Rule

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

Simplify

\frac{3}{2} \cdot \frac{2}{3} x^{\frac{3}{2}} : x^{\frac{3}{2}}

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

Add a constant to the solution

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

\frac{d}{d x} (2 a x - x^{2})

x \to 0 lim (\frac{cos ( 4 x ) - 1}{x})

x \to 0.1 lim (\frac{5 sin ( x )}{x})

x \to 6 lim (\frac{x ^{2} - 3 x - 18}{x - 6})

\int_{0}^{3} (x^{2} - 2 x) d x