5.5 The Substitution Rule/5

\begin{align} Failed to parse (syntax error): {\displaystyle \int \cos^{3}{(\theta)}\sin{(\theta)}d{(\theta)} \text{,} \quad u=\cos{(\theta)}\\[2ex] } \end{align}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=\cos {(\theta )}\\[2ex]du&=-\sin {(\theta )}d{(\theta )}\\[2ex]-du&=\sin {(\theta )}d{(\theta )}\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 \cos^{3}{(\theta)}\sin{(\theta)}d{(\theta)} &= -\int u^{3}du \\[2ex] &= \frac{-u^{4}}{4} + C = \frac{-\cos^{4}{(\theta)}}{4} + C \\[2ex] &= \frac{-1}{4}\cos^{4}{(\theta)} + C \end{align} }