5.5 The Substitution Rule/63
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_{0}^{a} x\,\cdot \sqrt{x^2+a^2}dx}
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+ a^2\\[2ex] du &=2xdx \\[2ex] \frac{1}{2}du &= xdx \\[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} \frac{1}{2} \int_{a^2}^{2a^2} \sqrt{u}\,\cdot du = \frac{1}{2}\,\cdot \frac{a^{\frac{1}{2}+1}}{\frac{1}{2}+1}\bigg|_{a^2}^{2a^2} \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} \frac{1}{2}\,\cdot \frac{2}{3}\,\cdot\ u^\frac{3}{2}\bigg|_{a^2}^{2a^2} = \frac{1}{3} \left(2a^{2}\right)^\frac{3}{2}- \frac{1}{3} \left(a^{2}\right)^\frac{3}{2} \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} = \frac{1}{3}\,\cdot 2^\frac{3}{2}\,\cdot {a^3}-\frac{1}{3} {a^3} =\frac{1}{3}\left(2^\frac{3}{2} -1 \right) {a^3} \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} \frac{1}{3} \left(2\sqrt{2}-1\right) {a^3} \end{align} }