5.5 The Substitution Rule/35

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\ \int {\frac {sin2x}{1+cos^{2}x}}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} let \; u &=1 + cos^2x \\[2ex] du &= 2cosx \;\cdot (-sinx)\;dx \\[2ex] -du & = 2sin(x)cos(x)\;dx & \\[2ex] -du & = sin(2x)dx & \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 \frac{sin 2 x}{1 + cos^2x} dx\;=\; -\ \int \frac {du}{u}\;=\;-ln( 1 + u) + c\;=\;-| 1 + cos^2x| + c \end{align} }