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

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

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

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

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

Solution steps

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

Simplify

x^{\frac{3}{2}} \frac{1}{x} : x^{\frac{1}{2}}

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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