5.5 The Substitution Rule/11: Difference between revisions
No edit summary |
No edit summary |
||
| Line 19: | Line 19: | ||
\int (x+1)\sqrt{2x+x^{2}}dx = \frac{1}{2}\int\sqrt{u}du = \frac{1}{2}\int u^{\frac{1}{2}}du \\[2ex] | \int (x+1)\sqrt{2x+x^{2}}dx = \frac{1}{2}\int\sqrt{u}du = \frac{1}{2}\int u^{\frac{1}{2}}du \\[2ex] | ||
&= \frac{1]{2}\left(\frac{2u^{3}{2}}{3})\right + C | |||
&= \frac{1}{3}\(u)^{\frac{3}{2}} + C | &= \frac{1}{3}\(u)^{\frac{3}{2}} + C | ||
| Line 26: | Line 28: | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 21:16, 22 September 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 (x+1)\sqrt{2x+x^{2}}dx }
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=2x+x^{2}\\[2ex]du&=2+2xdx\\[2ex]{\frac {1}{2}}du&=x+1\end{aligned}}}
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 (x+1)\sqrt{2x+x^{2}}dx = \frac{1}{2}\int\sqrt{u}du = \frac{1}{2}\int u^{\frac{1}{2}}du \\[2ex] &= \frac{1]{2}\left(\frac{2u^{3}{2}}{3})\right + C &= \frac{1}{3}\(u)^{\frac{3}{2}} + C \end{align} }