What is the integral of (0.3)/(rln(r)) ?

The integral of (0.3)/(rln(r)) is 0.3ln|ln(r)|+C

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integral of (0.3)/(rln(r))

\int \frac{0.3}{r ln ( r )} d r

0.3 ln ∣ ln (r) ∣ + C

Solution steps

\int \frac{0.3}{r ln ( r )} d r

Take the constant out:

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

= 0.3 \cdot \int \frac{1}{r ln ( r )} d r

Apply u-substitution

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

= 0.3 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 0.3 ln ∣ u ∣

Substitute back

u = ln (r)

= 0.3 ln ∣ ln (r) ∣

Add a constant to the solution

= 0.3 ln ∣ ln (r) ∣ + C

\int \frac{1}{u u ^{2} - 1} d u

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

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

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

\int 3 ln (x) + 3 d x

What is the integral of (0.3)/(rln(r)) ?
The integral of (0.3)/(rln(r)) is 0.3ln|ln(r)|+C