What is the integral of 6/(xln(7x)) ?

The integral of 6/(xln(7x)) is 6ln|ln(7x)|+C

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integral of 6/(xln(7x))

\int \frac{6}{x ln ( 7 x )} d x

6 ln ∣ ln (7 x) ∣ + C

Solution steps

\int \frac{6}{x ln ( 7 x )} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ln ( 7 x )} d x

Apply u-substitution

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

= 6 \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

= 6 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 6 ln ∣ v ∣

Substitute back

= 6 ln ∣ ln (7 x) ∣

Add a constant to the solution

= 6 ln ∣ ln (7 x) ∣ + C

\frac{d y}{d x} = x - 2.5 y

1.5 (1 + e^{- 0.2 t})

x \to 0 lim ((1 - 4 x)^{\frac{6}{x}})

f (x) = 2 cos (3 x) + 3 e^{- 0.25 x}

(x, y) \to (0, 0) lim (0)

What is the integral of 6/(xln(7x)) ?
The integral of 6/(xln(7x)) is 6ln|ln(7x)|+C