5.5 The Substitution Rule/7: Difference between revisions
Osbeenb61996 (talk | contribs) No edit summary |
No edit summary |
||
| (45 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
<math> | |||
\int x\sin{(x^{2})}dx | |||
</math> | |||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
u &=x^{2} \\[2ex] | |||
du &=2xdx \\[2ex] | |||
\frac{1}{2}du &=dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int x\sin{(x^{2})}dx &=\frac{1}{2}\int\sin{(u)}du \\[2ex] | |||
&= -\frac{1}{2}\cos{(u)}+C \\[2ex] | |||
&= -\frac{1}{2}\cos{(x^{2})}+C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 20:02, 7 September 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 x\sin{(x^{2})}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^{2} \\[2ex] du &=2xdx \\[2ex] \frac{1}{2}du &=dx \\[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 x\sin{(x^{2})}dx &=\frac{1}{2}\int\sin{(u)}du \\[2ex] &= -\frac{1}{2}\cos{(u)}+C \\[2ex] &= -\frac{1}{2}\cos{(x^{2})}+C \end{align} }