What is the integral of 1/(x(5+9ln(x))) ?

The integral of 1/(x(5+9ln(x))) is 1/9 ln|5+9ln(x)|+C

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integral of 1/(x(5+9ln(x)))

\int \frac{1}{x ( 5 + 9 ln ( x ) )} d x

\frac{1}{9} ln ∣ 5 + 9 ln (x) ∣ + C

Solution steps

\int \frac{1}{x ( 5 + 9 ln ( x ) )} d x

Apply u-substitution

: \int \frac{1}{9 u} d u

= \int \frac{1}{9 u} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{9} ln ∣ u ∣

Substitute back

u = 5 + 9 ln (x)

= \frac{1}{9} ln ∣ 5 + 9 ln (x) ∣

Add a constant to the solution

= \frac{1}{9} ln ∣ 5 + 9 ln (x) ∣ + C

x \to 0 lim ((1 - 7 x)^{\frac{5}{x}})

g (x) = \frac{ln ( x )}{x ^{2}}

\frac{d}{d x} ((ln (x))^{13})

(8 x^{2} + 9) (x^{2} - \frac{1}{x})

6 x^{2} - 4 x + 5

What is the integral of 1/(x(5+9ln(x))) ?
The integral of 1/(x(5+9ln(x))) is 1/9 ln|5+9ln(x)|+C