What is the integral of 1/((x(sqrt(ln(x))))) ?

The integral of 1/((x(sqrt(ln(x))))) is 2sqrt(ln(x))+C

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integral of 1/((x(sqrt(ln(x)))))

integral

\frac{1}{( x ( ln ( x ) ) )}

2 ln (x) + C

Solution steps

\int \frac{1}{x ln ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = ln (x)

= 2 ln^{\frac{1}{2}} (x)

Apply radical rule:

= 2 ln (x)

Add a constant to the solution

= 2 ln (x) + C

u^{- 1}

\frac{( x ) ^{\frac{1}{2}}}{( a - x ) ^{\frac{1}{2}}}

4 y + 1

sec^{2} (y) tan (tan (y))

ln (4 - 2 x)

What is the integral of 1/((x(sqrt(ln(x))))) ?
The integral of 1/((x(sqrt(ln(x))))) is 2sqrt(ln(x))+C