5.5 The Substitution Rule/54

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{0}^{\sqrt {\pi }}x\cos {x^{2}}\,dx}

${\begin{aligned}u&=4+3x\\[2ex]du&=3\,dx\\[2ex]{\frac {1}{3}}du&=dx\\[2ex]\end{aligned}}$

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} \int_{0}^{7} \sqrt{4+3x}\,dx = \int_{4}^{25}\sqrt{u}\,du\\[2ex] &= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] &= -\cos{(u)} + C \\[2ex] &= -\cos{(\ln{(x)})} + C \end{align} }