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

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

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

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

\int x^{2 n - 1} d x

sin (3 x)

\int \frac{( 2 x + 3 )}{x ^{2} + 2 x + 5} d x

\int \frac{1}{5 x lo g _{3} ( x )} d x

\int \frac{2 + ln ( x )}{x} d x

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