5.5 The Substitution Rule/11: Difference between revisions
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\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 | &= \frac{1}{2}({\frac{2u^\frac{3}{2}}{3}}) + C \\[2ex] | ||
&= \frac{1}{3}\(u)^{\frac{3}{2}} + C \\[2ex] | &= \frac{1}{3}\(u)^{\frac{3}{2}} + C \\[2ex] | ||
Revision as of 21:24, 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}({\frac{2u^\frac{3}{2}}{3}}) + C \\[2ex] &= \frac{1}{3}\(u)^{\frac{3}{2}} + C \\[2ex] \end{align} }