5.5 The Substitution Rule/67: Difference between revisions

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<math>\int_{e}^{e^4}\frac{dx}{x\sqrt{lnx}}</math> = <math>\int_{1}^{4}\frac{1}{u}du</math> = <math>\int_{1}^{4}u^{-1/2}du</math> = <math>\frac{u^{1/2}}{1/2}\bigg|_{1}^{4}</math> = = <math>{2u}^{1/2}\bigg|_{1}^{4}</math> = <math>[2(4)^{1/2}]-[2(1)^{1/2}</math>
<math>\int_{e}^{e^4}\frac{dx}{x\sqrt{lnx}}</math> = <math>\int_{1}^{4}\frac{1}{u}du</math> = <math>\int_{1}^{4}u^{-1/2}du</math> = <math>\frac{u^{1/2}}{1/2}\bigg|_{1}^{4}</math> = = <math>{2u}^{1/2}\bigg|_{1}^{4}</math> = <math>2(4)^{1/2}-2(1)^{1/2}</math>

Revision as of 20:04, 3 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}^{e^4}\frac{dx}{x\sqrt{lnx}}} = 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_{1}^{4}\frac{1}{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 \int_{1}^{4}u^{-1/2}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 \frac{u^{1/2}}{1/2}\bigg|_{1}^{4}} = = 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 {2u}^{1/2}\bigg|_{1}^{4}} = 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 2(4)^{1/2}-2(1)^{1/2}}

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