What is the integral of 1/(\sqrt[4]{t^3)} ?

The integral of 1/(\sqrt[4]{t^3)} is 4\sqrt[4]{t}+C

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integral of 1/(\sqrt[4]{t^3)}

\int \frac{1}{4 t ^{3}} d t

4 4 t + C

Solution steps

\int \frac{1}{4 t ^{3}} d t

4 t^{3} = t^{\frac{3}{4}},

assuming

t \geq 0

= \int \frac{1}{t ^{\frac{3}{4}}} d t

Apply the Power Rule

: 4 t^{\frac{1}{4}}

= 4 t^{\frac{1}{4}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 4 4 t

Add a constant to the solution

= 4 4 t + C

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What is the integral of 1/(\sqrt[4]{t^3)} ?
The integral of 1/(\sqrt[4]{t^3)} is 4\sqrt[4]{t}+C