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

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

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

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

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

Solution steps

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

x \to 3 lim (\frac{1}{x + 2})

x \to 0 - lim (2 + 3 e^{- \frac{3}{x}})

o f - 5 sin (x)

x \to - 3 lim (\frac{2 - x}{3 - x})

\frac{\partial}{\partial x} (2 x (2 + y)^{- 1})

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