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23-05-2018
Mathematics

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∫(sec(lnx)tan(lnx)) /x

seclnxtanlnx x class=

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LammettHash LammettHash

23-05-2018

Substitute [tex]y=\ln x\implies\mathrm dy=\dfrac{\mathrm dx}x[/tex], then the integral becomes

[tex]\displaystyle\int\frac{\sec(\ln x)\tan(\ln x)}x\,\mathrm dx=\int\sec y\tan y\,\mathrm dy[/tex]
[tex]=\sec y+C[/tex]

[tex]=\sec(\ln x)+C[/tex]

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