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

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

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

\int_{1}^{2} \frac{1}{x ln ( x )} d x

2 ln (2)

Decimal Notation

1.66510 \dots

Solution steps

\int_{1}^{2} \frac{1}{x ln ( x )} d x

Apply u-substitution

: \int_{0}^{l n (2)} \frac{1}{u} d u

= \int_{0}^{l n (2)} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{l n (2)}

= [2 u^{\frac{1}{2}}]_{0}^{l n (2)}

Apply radical rule:

= [2 u]_{0}^{l n (2)}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

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