What is the integral of \sqrt[m]{x^n} ?

The integral of \sqrt[m]{x^n} is (mx^{(n+m)/m})/(n+m)+C

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integral of \sqrt[m]{x^n}

\frac{m x ^{\frac{n + m}{m}}}{n + m} + C

Solution steps

Apply exponent rule:

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

= \int x^{\frac{n}{m}} d x

Apply the Power Rule

= \frac{m x ^{\frac{n + m}{m}}}{n + m}

Add a constant to the solution

= \frac{m x ^{\frac{n + m}{m}}}{n + m} + C

What is the integral of \sqrt[m]{x^n} ?
The integral of \sqrt[m]{x^n} is (mx^{(n+m)/m})/(n+m)+C