Final answer to the problem
$\left(\frac{12}{7}\sqrt[3]{x^{7}}+\frac{1}{2}\sqrt[3]{x^{2}}\right)\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)+3\sqrt[6]{x}+\frac{72}{77}\sqrt[6]{x^{11}}+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^2}}{3x}\right)dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^2}}{3x}\right)dx$
Learn how to solve integrals of rational functions problems step by step online. Integrate the function (2/(x^1/2)-3^1/2)(4xx^1/3+(x^2^1/3)/(3x)). Find the integral. Simplifying. We can solve the integral \int\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^2}}{3x}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.
Final answer to the problem
$\left(\frac{12}{7}\sqrt[3]{x^{7}}+\frac{1}{2}\sqrt[3]{x^{2}}\right)\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)+3\sqrt[6]{x}+\frac{72}{77}\sqrt[6]{x^{11}}+C_0$