5.5 The Substitution Rule/45: Difference between revisions
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\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_{}^{} \left(\frac{u}{\sqrt[4](u)} - \frac{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) | &=\int_{}^{} \left(u^{\frac{3}{4}} - 2u^{-\frac{1}{u}} \right) | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:12, 7 September 2022
![{\displaystyle \int _{}^{}\left({\frac {x}{\sqrt[{4}]{x+2}}}\right)dx}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/027085a0358008373de484ce727072a0833147c6)
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} u &= x+2 \\[2ex] du &=1dx \\[2ex] u-2 &=x \\[2ex] \end{align} }
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_{}^{} \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{align} }