5.4 Indefinite Integrals and the Net Change Theorem/6: Difference between revisions
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&= \left(\frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1}\right) + \left(\frac{x^{\frac{2}{3}+1}}{\frac{2}{3}+1}\right) + C\\[2ex] | &= \left(\frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1}\right) + \left(\frac{x^{\frac{2}{3}+1}}{\frac{2}{3}+1}\right) + C\\[2ex] | ||
&= 3\frac{x^{\frac{4}{3}}{4} | |||
\end{align} | \end{align} | ||
</math> | </math> |
Revision as of 18:02, 26 August 2022
Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int\left(\sqrt{x^3}+\sqrt[3]{x^2}\right)dx &= \int\left(x^{\frac{1}{3}}+x^{\frac{2}{3}}\right)dx \\[2ex] &= \left(\frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1}\right) + \left(\frac{x^{\frac{2}{3}+1}}{\frac{2}{3}+1}\right) + C\\[2ex] &= 3\frac{x^{\frac{4}{3}}{4} \end{align} }