What is the integral of 3/(x(ln(3x))^2) ?

The integral of 3/(x(ln(3x))^2) is -3/(ln(3x))+C

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integral of 3/(x(ln(3x))^2)

\int \frac{3}{x ( ln ( 3 x ) ) ^{2}} d x

- \frac{3}{ln ( 3 x )} + C

Solution steps

\int \frac{3}{x ( ln ( 3 x ) ) ^{2}} 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 ( 3 x ) ) ^{2}} d x

Simplify

= 3 \cdot \int \frac{1}{x ln ^{2} ( 3 x )} d x

Apply u-substitution

: \int \frac{1}{u ln ^{2} ( u )} d u

= 3 \cdot \int \frac{1}{u ln ^{2} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= 3 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 3 (- \frac{1}{v})

Substitute back

= 3 (- \frac{1}{ln ( 3 x )})

Simplify

3 (- \frac{1}{ln ( 3 x )}) : - \frac{3}{ln ( 3 x )}

= - \frac{3}{ln ( 3 x )}

Add a constant to the solution

= - \frac{3}{ln ( 3 x )} + C

y = (8 x + 5)^{3}

\int b x e^{3 x y} d y

\frac{d}{d x} (x^{- a})

\int (\frac{x + 7}{x ^{2} + 4}) d x

\frac{d}{d x} (\frac{4}{3} x)

What is the integral of 3/(x(ln(3x))^2) ?
The integral of 3/(x(ln(3x))^2) is -3/(ln(3x))+C