I'm not sure about answer.It looks very strange.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

[tex]\int_{1}^{e}\frac{dx}{x\sqrt{1+ln^2x}}[/tex]

3. The attempt at a solution

for u=lnx-->u'=1/x

[tex]\int \frac{du}{\sqrt{1+u^2}}[/tex]

substituting [tex]u=tan\theta[/tex]

[tex]=\int \frac{d\theta}{cos\theta}=ln|sec\theta+tan\theta|[/tex]

[tex]\int_{1}^{e}\frac{dx}{x\sqrt{1+ln^2x}}=ln|\sqrt{-1}|[/tex]

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# Homework Help: Integration by Trigonometric Substitution.

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