What is the integral of (30)/(x(ln(5x))^2) ?

The integral of (30)/(x(ln(5x))^2) is -(30)/(ln(5x))+C

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integral of (30)/(x(ln(5x))^2)

\int \frac{30}{x ( ln ( 5 x ) ) ^{2}} d x

- \frac{30}{ln ( 5 x )} + C

Solution steps

\int \frac{30}{x ( ln ( 5 x ) ) ^{2}} d x

Take the constant out:

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

= 30 \cdot \int \frac{1}{x ( ln ( 5 x ) ) ^{2}} d x

Simplify

= 30 \cdot \int \frac{1}{x ln ^{2} ( 5 x )} d x

Apply u-substitution

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

= 30 \cdot \int \frac{1}{u ln ^{2} ( u )} d u

Apply u-substitution

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

= 30 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 30 (- \frac{1}{v})

Substitute back

= 30 (- \frac{1}{ln ( 5 x )})

Simplify

30 (- \frac{1}{ln ( 5 x )}) : - \frac{30}{ln ( 5 x )}

= - \frac{30}{ln ( 5 x )}

Add a constant to the solution

= - \frac{30}{ln ( 5 x )} + C

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What is the integral of (30)/(x(ln(5x))^2) ?
The integral of (30)/(x(ln(5x))^2) is -(30)/(ln(5x))+C