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>2</math> | <math>\int_{e}^{e^4}\frac{dx}{x\sqrt{lnx}}</math> | ||
<math>u</math> = <math>lnx</math> | |||
<math>du</math> = <math>\frac{1}{x}</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> | |||
Latest revision as of 03:31, 8 September 2022
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