5.5 The Substitution Rule/63

$\int _{0}^{a}x*{\sqrt {x^{2}+a^{2}}}dx$

${\begin{aligned}u&=x^{2}+a^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=xdx\\[2ex]\end{aligned}}$

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} \frac{1}{2} \int_{a^2}^{2a^2} \sqrt{u}\,\cdot du = \frac{1}{2}\,\cdot \frac{a^{\frac{1/2}+1}{1/2+1} \bigg|_{2a^2}^{a^2} \end{align} }