5.4 Indefinite Integrals and the Net Change Theorem/6: Difference between revisions
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\int\left(\sqrt{x^3}+\sqrt[3]{x^2}\right)dx &= \int\left(x^{\frac{1}{3}}+x^{\frac{2}{3}}\right)dx \\[2ex] | \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)\\[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] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 18:01, 26 August 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\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]\end{aligned}}}