7.1 Integration By Parts/13

$\int t\sec ^{2}\left(2t\right)dt$

$u=t\qquad dv=\sec ^{2}\left(2t\right)\qquad \int \sec ^{2}\left(2t\right)dt$

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 du = dt \qquad v = \frac{1}{2}\tan\left(2t\right)}

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 t\sec^2\left(2t\right) dt = \frac{1}{2}\tan\left(2t\right)-\frac{1}{2}\int\tan\left(2t\right)dt = \frac{1}{2}\tan\left(2t\right)-\frac{1}{4}\int\tan\left(u\right)du = \frac{1}{2}\tan\left(2t\right)-\frac{1}{4}\ln|\sec2t|+c }

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=2t \\[2ex] & du=2dt \\[2ex] & \frac{du}{2}=dt \\[2ex] \end{align} }