5.5 The Substitution Rule/3

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{2}{\sqrt {x^{3}+1}}dx}

${\begin{aligned}u&=x^{3}+1\\[2ex]du&=3x^{2}dx\end{aligned}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int {\frac {1}{3}}du{\sqrt {u}}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}{\frac {1}{3}}\int du(u^{\frac {1}{2}})\\[2ex]={\frac {1}{2}}u^{\frac {3}{2}}\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 \frac{1}{2}(x^3+1)^\frac{3}{2} +C }