What is the integral from e to e^3 of 1/(x(ln(x))^4) ?

The integral from e to e^3 of 1/(x(ln(x))^4) is 26/81

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integral from e to e^3 of 1/(x(ln(x))^4)

\int_{e}^{e^{3}} \frac{1}{x ( ln ( x ) ) ^{4}} d x

\frac{26}{81}

Decimal

0.32098 \dots

Solution steps

\int_{e}^{e^{3}} \frac{1}{x ( ln ( x ) ) ^{4}} d x

Apply u-substitution

= \int_{1}^{3} \frac{1}{u ^{4}} d u

Apply the Power Rule

= [- \frac{1}{3 u ^{3}}]_{1}^{3}

Compute the boundaries:

\frac{26}{81}

= \frac{26}{81}

What is the integral from e to e^3 of 1/(x(ln(x))^4) ?
The integral from e to e^3 of 1/(x(ln(x))^4) is 26/81