What is the integral from 1 to e of 1/(xsqrt(ln(x))) ?

The integral from 1 to e of 1/(xsqrt(ln(x))) is 2

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integral from 1 to e of 1/(xsqrt(ln(x)))

\int_{1}^{e} \frac{1}{x ln ( x )} d x

2

Solution steps

\int_{1}^{e} \frac{1}{x ln ( x )} d x

Apply u-substitution

: \int_{0}^{1} \frac{1}{u} d u

= \int_{0}^{1} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{1}

= [2 u^{\frac{1}{2}}]_{0}^{1}

Apply radical rule:

a^{\frac{1}{n}} = n a

= [2 u]_{0}^{1}

Compute the boundaries:

2

= 2

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What is the integral from 1 to e of 1/(xsqrt(ln(x))) ?
The integral from 1 to e of 1/(xsqrt(ln(x))) is 2