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

The integral of 3/(xsqrt(ln(x))) is 6sqrt(ln(x))+C

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

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

6 ln (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

= 3 \cdot \int \frac{1}{u} d u

Apply the Power Rule

= 3 \cdot 2 u^{\frac{1}{2}}

Substitute back

u = ln (x)

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

Simplify

3 \cdot 2 ln^{\frac{1}{2}} (x) : 6 ln (x)

= 6 ln (x)

Add a constant to the solution

= 6 ln (x) + C

What is the integral of 3/(xsqrt(ln(x))) ?
The integral of 3/(xsqrt(ln(x))) is 6sqrt(ln(x))+C