7.1 Integration By Parts/13: Difference between revisions
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<math>\int t\sec^2\left(2t\right) dt </math> | <math>\int t\sec^2\left(2t\right) dt </math> | ||
<math>u = t \qquad dv = \sec^2\left(2t\right) | <math>u = t \qquad dv = \sec^2\left(2t\right) </math> <br><br> | ||
<math>du = dt \qquad v = \frac{1}{2}\tan\left(2t\right)</math> | <math>du = dt \qquad v = \frac{1}{2}\tan\left(2t\right)</math> | ||
<math> | |||
\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 | |||
</math> | |||
<math> | |||
\begin{align} | |||
& u=2t \\[2ex] | |||
& du=2dt \\[2ex] | |||
& \frac{du}{2}=dt \\[2ex] | |||
\end{align} | |||
</math> | |||
Latest revision as of 21:48, 16 December 2022
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 }
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 u = t \qquad dv = \sec^2\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} }