What is the integral from e to e^{10 of} 1/(xln(x)) ?

The integral from e to e^{10 of} 1/(xln(x)) is ln(10)

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integral from e to e^{10 of} 1/(xln(x))

\int_{e}^{e^{10}} \frac{1}{x ln ( x )} d x

ln (10)

Decimal Notation

2.30258 \dots

Solution steps

\int_{e}^{e^{10}} \frac{1}{x ln ( x )} d x

Apply u-substitution

: \int_{1}^{10} \frac{1}{u} d u

= \int_{1}^{10} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{10}

Compute the boundaries:

ln (10)

= ln (10)

\int_{0}^{2} y 2 y - y^{2} d y

\int_{1}^{2} x^{2} (x - 2)^{10} d x

\int_{1}^{e} (17 + ln (x))^{2} d x

\int_{0}^{3} x^{4} (9 - x^{2})^{\frac{3}{2}} d x

What is the integral from e to e^{10 of} 1/(xln(x)) ?
The integral from e to e^{10 of} 1/(xln(x)) is ln(10)