7.1 Integration By Parts/48: Difference between revisions
No edit summary |
No edit summary |
||
| Line 16: | Line 16: | ||
<math> | <math> | ||
\begin{align} | |||
\int_{}^{} \left(x^{n} e^{x} \right)dx = x^{n}e^{x} - \int_{}^{} \left(n x^{n-1}e^{x}\right)dx | \int_{}^{} \left(x^{n} e^{x} \right)dx &= x^{n}e^{x} - \int_{}^{} \left(n x^{n-1}e^{x}\right)dx | ||
&= x^{n}e^{x} - n \int_{}^{} \left(x^{n-1}e^{x}\right)dx | |||
\end{align} | |||
</math> | </math> | ||
Revision as of 20:04, 28 November 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_{}^{} \left(x^{n} e^{x} \right)dx = x^{n} e^{x} - n\int_{}^{} \left(x^{n-1} e^{x}\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 &= x^{n} \quad dv= e^{x} dx \\[2ex] du &=n x^{n-1} dx \quad v=e^x \\[2ex] \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_{}^{} \left(x^{n} e^{x} \right)dx &= x^{n}e^{x} - \int_{}^{} \left(n x^{n-1}e^{x}\right)dx &= x^{n}e^{x} - n \int_{}^{} \left(x^{n-1}e^{x}\right)dx \end{align} }