What is the integral of 1/(x(ln(x^6))^7) ?

The integral of 1/(x(ln(x^6))^7) is -1/(1679616ln^6(x))+C

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integral of 1/(x(ln(x^6))^7)

\int \frac{1}{x ( ln ( x ^{6} ) ) ^{7}} d x

- \frac{1}{1679616 ln ^{6} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ^{6} ) ) ^{7}} d x

Simplify

\frac{1}{x ( ln ( x ^{6} ) ) ^{7}} : \frac{1}{279936 x ln ^{7} ( x )}

= \int \frac{1}{279936 x ln ^{7} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{279936} \cdot \int \frac{1}{x ln ^{7} ( x )} d x

Apply u-substitution

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

= \frac{1}{279936} \cdot \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= \frac{1}{279936} (- \frac{1}{6 u ^{6}})

Substitute back

u = ln (x)

= \frac{1}{279936} (- \frac{1}{6 ln ^{6} ( x )})

Simplify

\frac{1}{279936} (- \frac{1}{6 ln ^{6} ( x )}) : - \frac{1}{1679616 ln ^{6} ( x )}

= - \frac{1}{1679616 ln ^{6} ( x )}

Add a constant to the solution

= - \frac{1}{1679616 ln ^{6} ( x )} + C

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What is the integral of 1/(x(ln(x^6))^7) ?
The integral of 1/(x(ln(x^6))^7) is -1/(1679616ln^6(x))+C