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The power of a product is equal to the product of it's factors raised to the same power
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$\int\left(\frac{2\sqrt[3]{x}-3x}{x}-2\right)\left(1+\frac{2x-\sqrt[3]{x}}{\sqrt[3]{x}}\right)dx$
Learn how to solve problems step by step online. Integrate int((((8x)^(1/3)-3x)/x-2)(1+(2x-x^(1/3))/(x^(1/3))))dx. The power of a product is equal to the product of it's factors raised to the same power. Rewrite the integrand \left(\frac{2\sqrt[3]{x}-3x}{x}-2\right)\left(1+\frac{2x-\sqrt[3]{x}}{\sqrt[3]{x}}\right) in expanded form. Expand the integral \int\left(\frac{2\sqrt[3]{x}-3x}{x}+\frac{7\sqrt[3]{x^{4}}-2\sqrt[3]{x^{2}}-6x^2}{\sqrt[3]{x^{4}}}-2+\frac{-4x+2\sqrt[3]{x}}{\sqrt[3]{x}}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2\sqrt[3]{x}-3x}{x}dx results in: 6\sqrt[3]{x}-3x.
