What is the integral of 1/(x(ln(x))^{7/3)} ?

The integral of 1/(x(ln(x))^{7/3)} is -3/(4ln^{4/3)(x)}+C

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integral of 1/(x(ln(x))^{7/3)}

\int \frac{1}{x ( ln ( x ) ) ^{\frac{7}{3}}} d x

- \frac{3}{4 ln ^{\frac{4}{3}} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{\frac{7}{3}}} d x

Apply u-substitution

: \int \frac{1}{u ^{\frac{7}{3}}} d u

= \int \frac{1}{u ^{\frac{7}{3}}} d u

Apply the Power Rule

: - \frac{3}{4 u ^{\frac{4}{3}}}

= - \frac{3}{4 u ^{\frac{4}{3}}}

Substitute back

u = ln (x)

= - \frac{3}{4 ln ^{\frac{4}{3}} ( x )}

Add a constant to the solution

= - \frac{3}{4 ln ^{\frac{4}{3}} ( x )} + C

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What is the integral of 1/(x(ln(x))^{7/3)} ?
The integral of 1/(x(ln(x))^{7/3)} is -3/(4ln^{4/3)(x)}+C