What is the integral of sqrt(y^3) ?

The integral of sqrt(y^3) is 2/5 y^{5/2}+C

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integral of sqrt(y^3)

\int y^{3} d y

\frac{2}{5} y^{\frac{5}{2}} + C

Solution steps

\int y^{3} d y

y^{3} = y^{\frac{3}{2}},

assuming

y \geq 0

= \int y^{\frac{3}{2}} d y

Apply the Power Rule

: \frac{2}{5} y^{\frac{5}{2}}

= \frac{2}{5} y^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} y^{\frac{5}{2}} + C

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