Final Answer
$\frac{x^{3}}{3}-4\sqrt{x}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{x^3-2\sqrt{x}}{x}dx$
Specify the solving method
1
Expand the fraction $\frac{x^3-2\sqrt{x}}{x}$ into $2$ simpler fractions with common denominator $x$
$\int\left(\frac{x^3}{x}+\frac{-2\sqrt{x}}{x}\right)dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{x^3}{x}+\frac{-2\sqrt{x}}{x}\right)dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3-2x^1/2)/x)dx. Expand the fraction \frac{x^3-2\sqrt{x}}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions. Expand the integral \int\left(x^{2}-2x^{-\frac{1}{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.
Final Answer
$\frac{x^{3}}{3}-4\sqrt{x}+C_0$