5.5 The Substitution Rule/25: Difference between revisions
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<math> | <math> | ||
u= | u=1+e^x | ||
</math> | |||
<math> | |||
du=e^xdx | |||
</math> | |||
<math> | |||
\int e^x\sqrt{1+e^x}dx=\int\sqrt{u}du | |||
</math> | |||
<math> | |||
\sqrt{u}du=\frac{2u^{2/3}}{3}+C | |||
</math> | |||
<math> | |||
=\frac{2}{3}(e^x+1)^{3/2} | |||
</math> | </math> | ||
Latest revision as of 19:10, 2 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 e^x\sqrt{1+e^x}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 u=1+e^x }
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=e^xdx }
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 e^x\sqrt{1+e^x}dx=\int\sqrt{u}du }
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 \sqrt{u}du=\frac{2u^{2/3}}{3}+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 =\frac{2}{3}(e^x+1)^{3/2} }