What is the integral of 1/(xln(x^3)) ?

The integral of 1/(xln(x^3)) is 1/3 ln(3|ln(x)|)+C

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integral of 1/(xln(x^3))

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

\frac{1}{3} ln (3 ∣ ln (x) ∣) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u ln ( u )} d u

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

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{3} ln ∣ v ∣

Substitute back

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

Simplify

\frac{1}{3} ln ln (x^{3}) : \frac{1}{3} ln (3 ∣ ln (x) ∣)

= \frac{1}{3} ln (3 ∣ ln (x) ∣)

Add a constant to the solution

= \frac{1}{3} ln (3 ∣ ln (x) ∣) + C

\frac{\partial}{\partial x} (e^{x y} cos (y))

\frac{d y}{d x} = \frac{3 y ^{3}}{x ^{2}}, y (3) = 1

(2 sin (x))^{^{'}}

(- 29, - 40), (- 28, 3)

x \to - \infty lim (x^{- 5})

What is the integral of 1/(xln(x^3)) ?
The integral of 1/(xln(x^3)) is 1/3 ln(3|ln(x)|)+C