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

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

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

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

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

Solution steps

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

(x^{3})^{\frac{1}{2}} = x^{\frac{3}{2}},

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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