5.5 The Substitution Rule/5

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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 \cos^{3}{(\theta)}\sin{(\theta)}d{(\theta)} \text{,} \quad u=\cos{(\theta)} }

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 &=\cos{(\theta)} \\[2ex] du &=-\sin{(\theta)}d{(\theta)} \\[2ex] -du &=\sin{(\theta)}d{(\theta)} \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 \cos^{3}{(\theta)}\sin{(\theta)}d{(\theta)} &= -\int u^{3}du \\[2ex] \end{align} }

&= \frac{-u^{4}}{4} + C = \frac{-\cos^{4}{(\theta)}}{4} + C &= \frac{-1}{4}\cos^{4}{(\theta)} + C

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