5.4 Indefinite Integrals and the Net Change Theorem/11: Difference between revisions
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\int\left({}^{}\frac{x^3-2\sqrt{x}}{x}\right)dx &= \int\left({}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}\right)dx | \int\left({}^{}\frac{x^3-2\sqrt{x}}{x}\right)dx &= \int\left({}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}\right)dx | ||
&= \left x^2-2x^\frac{-1}{2}\right)dx | &= \left x^2-2x^\frac{-1}{2}\right)dx | ||
&= \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}}+C &= \frac{1}{3}x^3-4\sqrt{x}+ C | &= \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}} + C | ||
&= \frac{1}{3}x^3-4\sqrt{x}+ C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 19:07, 30 August 2022
Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int\left({}^{}\frac{x^3-2\sqrt{x}}{x}\right)dx &= \int\left({}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}\right)dx &= \left x^2-2x^\frac{-1}{2}\right)dx &= \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}} + C &= \frac{1}{3}x^3-4\sqrt{x}+ C \end{align} }