Learn how to solve problems step by step online. Integrate int((2x)^(1/3)^2)dx. Simplify \left(\sqrt[3]{2x}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{3} and n equals 2. The power of a product is equal to the product of it's factors raised to the same power. The integral of a function times a constant (\sqrt[3]{\left(2\right)^{2}}) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as \frac{2}{3}.

Integrate int((2x)^(1/3)^2)dx