What is the integral of 1/2 x^{3/2} ?

The integral of 1/2 x^{3/2} is 1/5 x^{5/2}+C

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integral of 1/2 x^{3/2}

\int \frac{1}{2} x^{\frac{3}{2}} d x

\frac{1}{5} x^{\frac{5}{2}} + C

Solution steps

\int \frac{1}{2} x^{\frac{3}{2}} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

= \frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{1}{2} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{1}{5} x^{\frac{5}{2}}

= \frac{1}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{5} x^{\frac{5}{2}} + C

\int (1 - x^{- 2}) x + x^{- 1} d x

\int \frac{1}{x + 1 ^{5}} d x

\int (3 z^{2} + 1) arctan (z)

\int 2 x (x^{3} + 1) d x

\int 3 t e^{- s t} d t

What is the integral of 1/2 x^{3/2} ?
The integral of 1/2 x^{3/2} is 1/5 x^{5/2}+C