What is the integral of 1/(x(ln(x))^{10)} ?

The integral of 1/(x(ln(x))^{10)} is -1/(9ln^9(x))+C

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integral of 1/(x(ln(x))^{10)}

\int \frac{1}{x ( ln ( x ) ) ^{10}} d x

- \frac{1}{9 ln ^{9} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{10}} d x

Simplify

= \int \frac{1}{x ln ^{10} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{10}} d u

= \int \frac{1}{u ^{10}} d u

Apply the Power Rule

: - \frac{1}{9 u ^{9}}

= - \frac{1}{9 u ^{9}}

Substitute back

u = ln (x)

= - \frac{1}{9 ln ^{9} ( x )}

Add a constant to the solution

= - \frac{1}{9 ln ^{9} ( x )} + C

\frac{d}{d x} (\frac{tan ^{3} ( x )}{2 x + 1})

\int sin (4 - x) d x

x \to 0 lim (ln ∣ sin (x) ∣)

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

18 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

What is the integral of 1/(x(ln(x))^{10)} ?
The integral of 1/(x(ln(x))^{10)} is -1/(9ln^9(x))+C