What is the integral of 1/(x(ln(x^4))^5) ?

The integral of 1/(x(ln(x^4))^5) is -1/(4096ln^4(x))+C

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integral of 1/(x(ln(x^4))^5)

\int \frac{1}{x ( ln ( x ^{4} ) ) ^{5}} d x

- \frac{1}{4096 ln ^{4} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ^{4} ) ) ^{5}} d x

Apply u-substitution

: \int \frac{1}{4 u ln ^{5} ( u )} d u

= \int \frac{1}{4 u ln ^{5} ( u )} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u ln ^{5} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{5}} d v

= \frac{1}{4} \cdot \int \frac{1}{v ^{5}} d v

Apply the Power Rule

: - \frac{1}{4 v ^{4}}

= \frac{1}{4} (- \frac{1}{4 v ^{4}})

Substitute back

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

Simplify

\frac{1}{4} (- \frac{1}{4 ln ^{4} ( x ^{4} )}) : - \frac{1}{4096 ln ^{4} ( x )}

= - \frac{1}{4096 ln ^{4} ( x )}

Add a constant to the solution

= - \frac{1}{4096 ln ^{4} ( x )} + C

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What is the integral of 1/(x(ln(x^4))^5) ?
The integral of 1/(x(ln(x^4))^5) is -1/(4096ln^4(x))+C