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

= \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

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

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

x = \frac{( y - 3 ) ^{2}}{5}, x = 13 - y

\frac{d}{d x} (\frac{3}{4} x^{\frac{1}{2}})

\int_{0}^{8} \frac{9}{10 x ^{2} + 11 x + 1} d x