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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

Apply exponent rule:

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

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

Apply the Power Rule

= \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

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