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

The integral of 1/(x(ln(x))^5) is -1/(4ln^4(x))+C

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integral of 1/(x(ln(x))^5)

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

- \frac{1}{4 ln ^{4} ( x )} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{5}} d u

= \int \frac{1}{u ^{5}} d u

Apply the Power Rule

: - \frac{1}{4 u ^{4}}

= - \frac{1}{4 u ^{4}}

Substitute back

u = ln (x)

= - \frac{1}{4 ln ^{4} ( x )}

Add a constant to the solution

= - \frac{1}{4 ln ^{4} ( x )} + C

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 3 x^{3}))

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

e^{a x}

\frac{d}{d x} (\frac{1}{3 - x})

\int x ln (x + 2) d x

What is the integral of 1/(x(ln(x))^5) ?
The integral of 1/(x(ln(x))^5) is -1/(4ln^4(x))+C