What is the integral from e to e^2 of 1/(xln^3(x)) ?

The integral from e to e^2 of 1/(xln^3(x)) is 3/8

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integral from e to e^2 of 1/(xln^3(x))

\int_{e}^{e^{2}} \frac{1}{x ln ^{3} ( x )} d x

\frac{3}{8}

Decimal

0.375

Solution steps

\int_{e}^{e^{2}} \frac{1}{x ln ^{3} ( x )} d x

Apply u-substitution

: \int_{1}^{2} \frac{1}{u ^{3}} d u

= \int_{1}^{2} \frac{1}{u ^{3}} d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{3}{8}

= \frac{3}{8}

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What is the integral from e to e^2 of 1/(xln^3(x)) ?
The integral from e to e^2 of 1/(xln^3(x)) is 3/8