What is the integral of 1/(\sqrt[5]{t^3)} ?

The integral of 1/(\sqrt[5]{t^3)} is 5/2 t^{2/5}+C

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integral of 1/(\sqrt[5]{t^3)}

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

Solution steps

Apply exponent rule:

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

= \int \frac{1}{t ^{\frac{3}{5}}} d t

Apply the Power Rule

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

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

Add a constant to the solution

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

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What is the integral of 1/(\sqrt[5]{t^3)} ?
The integral of 1/(\sqrt[5]{t^3)} is 5/2 t^{2/5}+C