5.5 The Substitution Rule/9

$\int (3x-2)^{20}dx$

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

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 u^{20}\cdot\frac{1}{3}du \\[2ex] &= \frac{1}{3}\int u^{20}du &= \frac{1}{3}\cdot\frac{1}{20+1} u^{20+1} &= \frac{1}{3}\cdot\frac{1}{21} u^{21} &= \frac{1}{63} u^{21} + c &= \frac{1}{63} (3x-2)^{21} + c \end{align} }

</math> &= \frac{1}{63} (3x^21-2097152) + c </math>