What is the integral of 1/(sqrt(x^3)) ?

The integral of 1/(sqrt(x^3)) is -2/(sqrt(x))+C

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integral of 1/(sqrt(x^3))

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

- \frac{2}{x} + C

Solution steps

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

Apply exponent rule:

(a^{n})^{m} = a^{n \cdot m}

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

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

Apply the Power Rule

= - \frac{2}{x}

Add a constant to the solution

= - \frac{2}{x} + C

What is the integral of 1/(sqrt(x^3)) ?
The integral of 1/(sqrt(x^3)) is -2/(sqrt(x))+C