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
![{\displaystyle {\begin{aligned}u&=2x+x^{2}\\[2ex]du&=2+2xdx\\[2ex]{\frac {1}{2}}du&=x+1\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/457f3b114a8832535d70a7a359fc2dbe034c038b)
Failed to parse (unknown function "\begin{align}"): {\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} }