What is the integral of (22)/(xln(7x)) ?

The integral of (22)/(xln(7x)) is 22ln|ln(7x)|+C

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integral of (22)/(xln(7x))

\int \frac{22}{x ln ( 7 x )} d x

22 ln ∣ ln (7 x) ∣ + C

Solution steps

\int \frac{22}{x ln ( 7 x )} d x

Take the constant out:

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

= 22 \cdot \int \frac{1}{x ln ( 7 x )} d x

Apply u-substitution

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

= 22 \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

= 22 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 22 ln ∣ v ∣

Substitute back

= 22 ln ∣ ln (7 x) ∣

Add a constant to the solution

= 22 ln ∣ ln (7 x) ∣ + C

\frac{d}{d x} (x - 2 y)

\int x sin^{3} (x^{2}) cos^{2} (x^{2}) d x

t y^{^{'}} + 2 y = sin (t), y (\frac{π}{2}) = 9

\int x^{2} ln (x) d x

\int_{2}^{7} t^{4} ln (3 t) d t

What is the integral of (22)/(xln(7x)) ?
The integral of (22)/(xln(7x)) is 22ln|ln(7x)|+C