What is the integral of 3/(xln(x)) ?

The integral of 3/(xln(x)) is 3ln|ln(x)|+C

Popular >

integral of 3/(xln(x))

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

3 ln ∣ 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

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 ln ∣ u ∣

Substitute back

u = ln (x)

= 3 ln ∣ ln (x) ∣

Add a constant to the solution

= 3 ln ∣ ln (x) ∣ + C

\frac{d}{d x} (\frac{x ^{3}}{39} + \frac{13}{4 x})

f (x) = \frac{2}{t ^{3}}

\frac{d ^{2} y}{d x ^{2}}, x^{2} + y^{2} = 16

\frac{\partial}{\partial z} (x y + yz - x z)

1 - y^{2} d x = 1 - x^{2} d y