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

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

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

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

\frac{2}{3}

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{2}{3}

= \frac{2}{3}

\int_{- 1}^{1} (1 - x^{2}) - (x^{2} - 1) d x

\int_{\frac{π}{4}}^{\frac{π}{2}} x csc^{2} (x) d x

\int_{0}^{\frac{π}{4}} tan^{2} (t) d t

\int_{2}^{3} 3^{2 x} d x

\int_{- 2}^{1} 2 d x

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