Evaluate- - e e 2 dx - log x

∫_e^e^2dx/x log x=∫_e^e^21/x/log xdx= [ log(log x) ]_e^e^2 =log(log e^2) log(log e) =log(2 log e) log 1=log 2 ...

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Higher Order Derivatives

Evaluate: ∫ e...

Question

Evaluate: $\int_{e}^{e^{2}} \frac{d x}{x l o g x}$

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Solution

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\int_{e}^{e^{2}} \frac{d x}{x log x} .

I_{1} = \int_{e}^{e^{2}} \frac{d x}{l o g x}

I_{2} = \int_{1}^{2} \frac{e^{x}}{x} d x,

log (x + 3) + log (x - 3) = log 16

\int \frac{log x}{x^{2}} d x

\int \frac{log x}{x} d x

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