Final Answer
$\frac{15}{4}\sqrt[3]{x^{4}}-\frac{1}{2}x^2+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(5x^{\frac{1}{3}}-x\right)dx$
Specify the solving method
1
Expand the integral $\int\left(5\sqrt[3]{x}-x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int5\sqrt[3]{x}dx+\int-xdx$
Learn how to solve integrals of polynomial functions problems step by step online.
$\int5\sqrt[3]{x}dx+\int-xdx$
Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(5x^1/3-x)dx. Expand the integral \int\left(5\sqrt[3]{x}-x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5\sqrt[3]{x}dx results in: \frac{15}{4}\sqrt[3]{x^{4}}. The integral \int-xdx results in: -\frac{1}{2}x^2. Gather the results of all integrals.
Final Answer
$\frac{15}{4}\sqrt[3]{x^{4}}-\frac{1}{2}x^2+C_0$