What is the integral from e to e^3 of 5/(xln^2(x)) ?

The integral from e to e^3 of 5/(xln^2(x)) is 10/3

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integral from e to e^3 of 5/(xln^2(x))

\int_{e}^{e^{3}} \frac{5}{x ln ^{2} ( x )} d x

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

\int_{e}^{e^{3}} \frac{5}{x ln ^{2} ( x )} d x

Take the constant out:

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

= 5 \cdot \int_{e}^{e^{3}} \frac{1}{x ln ^{2} ( x )} d x

Apply u-substitution

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

= 5 \cdot \int_{1}^{3} \frac{1}{u ^{2}} d u

Apply the Power Rule

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

= 5 [- \frac{1}{u}]_{1}^{3}

Compute the boundaries:

\frac{2}{3}

= 5 \cdot \frac{2}{3}

Simplify

= \frac{10}{3}

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What is the integral from e to e^3 of 5/(xln^2(x)) ?
The integral from e to e^3 of 5/(xln^2(x)) is 10/3