5.4 Indefinite Integrals and the Net Change Theorem/11: Difference between revisions
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\begin{align} | \begin{align} | ||
\int\frac{x^3-2\sqrt{x}}{x}dx &= \int\left(\frac{x^3}{x}-\frac{2\sqrt{x}}{x}\right)dx = \int\left(x^2-2x^{1-\frac{1}{2}}\right)dx = | \int\frac{x^3-2\sqrt{x}}{x}dx &= \int\left(\frac{x^3}{x}-\frac{2\sqrt{x}}{x}\right)dx = \int\left(x^2-2x^{1-\frac{1}{2}}\right)dx = \int\left(x^2-2x^{1-\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 17:30, 13 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int {\frac {x^{3}-2{\sqrt {x}}}{x}}dx&=\int \left({\frac {x^{3}}{x}}-{\frac {2{\sqrt {x}}}{x}}\right)dx=\int \left(x^{2}-2x^{1-{\frac {1}{2}}}\right)dx=\int \left(x^{2}-2x^{1-{\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{aligned}}}