7.1 Integration By Parts/50: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
Prove | Prove | ||
<math> | <math> | ||
\int_{}^{} \sec^{n}x = \frac{\tanx \sec^{n-2}x}{n-1} | \int_{}^{} \sec^{n}x = \frac{\tanx \sec^{n-2}x}{n-1} | ||
</math> | </math> | ||
Revision as of 18:24, 29 November 2022
Prove 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_{}^{} \sec^{n}x = \frac{\tanx \sec^{n-2}x}{n-1} }
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_{}^{} \left(\ln(x)^{n}\right)dx }
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 = \ln(x)^{n} \quad dv= 1dx \\[2ex] &du =1dx \quad v=x \\[2ex] \end{align} }
<math> \begin{align}
\int_{}^{} \left(\ln(x)^{n}\right)dx &= x \ln(x)^{n} - \int_{}^{} \left((x \frac{n \ln(x)^{n-1}}{x}) \right)dx \\[2ex] &= x \ln(x)^{n} - \int_{}^{} \left(n \ln(x)^{n-1} \right)dx \\[2ex] &= x \ln(x)^{n} - n \int_{}^{} \left(\ln(x)^{n-1} \right)dx \\[2ex]