5.5 The Substitution Rule/54

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}^{\sqrt{\pi}} x\cos{(x^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 \\[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} \int_{0}^{\sqrt{\pi}} x\cos{(x^2)}\,dx &= \int_{0}^{\sqrt{\pi}} (xdx)\cos{(x^2)} = &= \int (\frac{1}{2}du)\cos{(u)} = \frac{1}{2}\int \cos{(u)}du \\[2ex] &= \frac{1}{2}\sin{(u)} + C \\[2ex] &= \frac{1}{2}\sin{(x^2)} + C \\[2ex] \end{align} }