5.5 The Substitution Rule/67: Difference between revisions
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<math>\begin{align}\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>2</math> | <math>\begin{align}\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>2\end{align}</math> | ||
Revision as of 20:08, 3 September 2022
Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align}\int_{e}^{e^4}\frac{dx}{x\sqrt{lnx}}} &= = &= = &=&=Failed to parse (syntax error): {\displaystyle 2\end{align}}
