What is the integral of 1/(x(ln(x))^4) ?

The integral of 1/(x(ln(x))^4) is -1/(3ln^3(x))+C

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integral of 1/(x(ln(x))^4)

\int \frac{1}{x ( ln ( x ) ) ^{4}} d x

- \frac{1}{3 ln ^{3} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{4}} d x

Apply u-substitution

: \int \frac{1}{u ^{4}} d u

= \int \frac{1}{u ^{4}} d u

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= - \frac{1}{3 u ^{3}}

Substitute back

u = ln (x)

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

Add a constant to the solution

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

\int \frac{x - 2}{( 2 x + 1 ) ( x + 3 )} d x

y = (7 x + 3) x^{2}

cos (x) (\frac{π}{2})

\frac{d}{d x} (5 ln ∣ x - e^{x} ∣)

z \to 1 lim (\frac{z}{2 i})

What is the integral of 1/(x(ln(x))^4) ?
The integral of 1/(x(ln(x))^4) is -1/(3ln^3(x))+C