5.5 The Substitution Rule/45: Difference between revisions
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\begin{align} | \begin{align} | ||
\int_{}^{} \left(\frac {x}{\sqrt[4]{x+2}}\right)dx &= \int_{}^{} \left(\frac{u-2}{\sqrt[4]{u}}\right) | \int_{}^{} \left(\frac {x}{\sqrt[4]{x+2}}\right)dx &= \int_{}^{} \left(\frac{u-2}{\sqrt[4]{u}}\right) | ||
&= \int_{}^{} (\frac{u}{\sqrt[4](u)} - \frac{2}{\sqrt[4](u)}) | &= \int_{}^{} \left(\frac{u}{\sqrt[4](u)} - \frac{2}{\sqrt[4](u)}\right) | ||
&= \int_{}^{} \left(u^{\frac{3}{4}} - 2u^{-\frac{1}{u}} \right) | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:11, 7 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_{}^{} \left(\frac {x}{\sqrt[4]{x+2}}\right)dx }
![{\displaystyle {\begin{aligned}u&=x+2\\[2ex]du&=1dx\\[2ex]u-2&=x\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7f086d72789e0c38347c5e01beecd53006c6b483)
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{}^{}\left({\frac {x}{\sqrt[{4}]{x+2}}}\right)dx&=\int _{}^{}\left({\frac {u-2}{\sqrt[{4}]{u}}}\right)&=\int _{}^{}\left({\frac {u}{{\sqrt[{4}]{(}}u)}}-{\frac {2}{{\sqrt[{4}]{(}}u)}}\right)&=\int _{}^{}\left(u^{\frac {3}{4}}-2u^{-{\frac {1}{u}}}\right)\end{aligned}}}