What is the integral of 1/(xln^4(ex)) ?

The integral of 1/(xln^4(ex)) is -1/(3ln^3(ex))+C

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integral of 1/(xln^4(ex))

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

- \frac{1}{3 ln ^{3} ( e x )} + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int \frac{1}{v ^{4}} d v

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

Apply the Power Rule

: - \frac{1}{3 v ^{3}}

= - \frac{1}{3 v ^{3}}

Substitute back

= - \frac{1}{3 ln ^{3} ( e x )}

Add a constant to the solution

= - \frac{1}{3 ln ^{3} ( e x )} + C

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What is the integral of 1/(xln^4(ex)) ?
The integral of 1/(xln^4(ex)) is -1/(3ln^3(ex))+C