5.4 Indefinite Integrals and the Net Change Theorem/11: Difference between revisions

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<math>\int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx </math>
<math>
<math>
\begin{align}
\int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx = x^2-2x^\frac{-1}{2}dx  
\int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx
</math>
&= \int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx &= x^2-2x^\frac{-1}{2}dx  
<math>
&= \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}}+C  
\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
 
\end{align}
</math>
</math>

Revision as of 19:13, 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 \int_{}^{}\frac{x^3-2\sqrt{x}}{x}dx }

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 \int_{}^{}\frac{x^3}{x}-\frac{2\sqrt{x}}{x}dx = x^2-2x^\frac{-1}{2}dx } 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 \frac{x^3}{3}-\frac{2x^\frac{1}{2}}{\frac{1}{2}}+C = \frac{1}{3}x^3-4\sqrt{x}+C }

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