What is the integral of 1/(xsqrt(ln(3x))) ?

The integral of 1/(xsqrt(ln(3x))) is 2sqrt(ln(3x))+C

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integral of 1/(xsqrt(ln(3x)))

\int \frac{1}{x ln ( 3 x )} d x

2 ln (3 x) + C

Solution steps

\int \frac{1}{x ln ( 3 x )} d x

Apply u-substitution

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

Apply the Power Rule

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

Substitute back

= 2 ln^{\frac{1}{2}} (3 x)

Apply radical rule:

= 2 ln (3 x)

Add a constant to the solution

= 2 ln (3 x) + C

What is the integral of 1/(xsqrt(ln(3x))) ?
The integral of 1/(xsqrt(ln(3x))) is 2sqrt(ln(3x))+C