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

Apply the Power Rule

= - \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

d er i v a t i v e \frac{e ^{3 x^{2}}}{5 x}

s l o p e (19.3) (20.3)

\frac{d}{d x} (e^{s i n (x)})

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

\frac{d}{d x} ((2 x^{3} - 12 x)^{\frac{4}{3}})

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