What is the integral of \sqrt[a]{x^2} ?

The integral of \sqrt[a]{x^2} is (ax^{(2+a)/a})/(2+a)+C

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integral of \sqrt[a]{x^2}

\int a x^{2} d x

\frac{a x ^{\frac{2 + a}{a}}}{2 + a} + C

Solution steps

\int a x^{2} d x

Apply exponent rule:

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

a x^{2} = x^{\frac{2}{a}}

= \int x^{\frac{2}{a}} d x

Apply the Power Rule

: \frac{a x ^{\frac{2 + a}{a}}}{2 + a}

= \frac{a x ^{\frac{2 + a}{a}}}{2 + a}

Add a constant to the solution

= \frac{a x ^{\frac{2 + a}{a}}}{2 + a} + C

f (x) = \frac{tan ( x ) - 1}{sec ( x )}

2 x^{2} y^{^{'}} = π y sin (\frac{π}{2 x})

x^{6 c o s (x)}

\frac{d}{d x} (8^{x^{4}})

\frac{x}{1 + x ^{2}}, \frac{x ^{2}}{1 + x ^{3}}, [0, 1]

What is the integral of \sqrt[a]{x^2} ?
The integral of \sqrt[a]{x^2} is (ax^{(2+a)/a})/(2+a)+C