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

The integral from e to e^3 of 1/(x(ln(x))^3) is 4/9

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

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

\frac{4}{9}

Decimal

0.44444 \dots

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= [- \frac{1}{2 u ^{2}}]_{1}^{3}

Compute the boundaries:

\frac{4}{9}

= \frac{4}{9}

What is the integral from e to e^3 of 1/(x(ln(x))^3) ?
The integral from e to e^3 of 1/(x(ln(x))^3) is 4/9