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

The integral of 1/(\sqrt[n]{t^m)} is (nt^{(-m+n)/n})/(-m+n)+C

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integral of 1/(\sqrt[n]{t^m)}

\int \frac{1}{n t ^{m}} d t

\frac{n t ^{\frac{- m + n}{n}}}{- m + n} + C

Solution steps

\int \frac{1}{n t ^{m}} d t

Apply exponent rule:

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

n t^{m} = t^{\frac{m}{n}}

= \int \frac{1}{t ^{\frac{m}{n}}} d t

Apply the Power Rule

: \frac{n t ^{\frac{- m + n}{n}}}{- m + n}

= \frac{n t ^{\frac{- m + n}{n}}}{- m + n}

Add a constant to the solution

= \frac{n t ^{\frac{- m + n}{n}}}{- m + n} + C

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What is the integral of 1/(\sqrt[n]{t^m)} ?
The integral of 1/(\sqrt[n]{t^m)} is (nt^{(-m+n)/n})/(-m+n)+C