5.4 Indefinite Integrals and the Net Change Theorem/11: Difference between revisions
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\int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx = \int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx | \int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx = \int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx | ||
&=x^2-2x^\frac{-1}{2}dx = \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}}+C | &=x^2-2x^\frac{-1}{2}dx = \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}}+C | ||
&=\frac{1}{3}x^3-4\sqrt{x}+C | &=\frac{1}{3}x^3-4\sqrt{x}+C | ||
Revision as of 19:08, 26 August 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx = \int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx &=x^2-2x^\frac{-1}{2}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} }