5.5 The Substitution Rule/2

$\int x^{3}(2+x^{4})^{5}dx{\text{,}}\quad u=2+x^{4}$

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

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 x^3(2+x^4)^5dx &= \int x^3dx(2+x^4) = \int \left(\frac{1}{4}du\right)(u) = \frac{1}{4}\int u\,du \\[2ex] &= \frac{1}{4}\cdot \frac{u^{1+1}}{1+1} + C = \frac{u^2}{8} + C = \frac{(2+x^4)^2}{8} + C \end{align} }