What is the integral of 4/(xln(7x)) ?

The integral of 4/(xln(7x)) is 4ln|ln(7x)|+C

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integral of 4/(xln(7x))

\int \frac{4}{x ln ( 7 x )} d x

4 ln ∣ ln (7 x) ∣ + C

Solution steps

\int \frac{4}{x ln ( 7 x )} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x ln ( 7 x )} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

= 4 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 4 ln ∣ v ∣

Substitute back

= 4 ln ∣ ln (7 x) ∣

Add a constant to the solution

= 4 ln ∣ ln (7 x) ∣ + C

\int \frac{x ^{3} - 1}{x + 1} d x

\int \frac{x ^{6}}{3} d x

\int e^{- x^{2} + 2} d x

\int \frac{x - 1}{x + 2} d x

\int (4 x^{2} + x + 3) d x

What is the integral of 4/(xln(7x)) ?
The integral of 4/(xln(7x)) is 4ln|ln(7x)|+C