What is the integral from 1 to e^5 of 1/(x(1+ln(x))) ?

The integral from 1 to e^5 of 1/(x(1+ln(x))) is ln(6)

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integral from 1 to e^5 of 1/(x(1+ln(x)))

\int_{1}^{e^{5}} \frac{1}{x ( 1 + ln ( x ) )} d x

ln (6)

Decimal Notation

1.79175 \dots

Solution steps

\int_{1}^{e^{5}} \frac{1}{x ( 1 + ln ( x ) )} d x

Apply u-substitution

: \int_{1}^{6} \frac{1}{u} d u

= \int_{1}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{6}

Compute the boundaries:

ln (6)

= ln (6)

\int - sin^{4} (x) d x

\int \frac{x ^{2} - 3 x - 5}{x} d x

\frac{d}{d x} (x^{2} + \frac{432}{x})

\int \frac{1}{3 + x} d x

f (x) = ln (6 x^{3} + e^{x})

What is the integral from 1 to e^5 of 1/(x(1+ln(x))) ?
The integral from 1 to e^5 of 1/(x(1+ln(x))) is ln(6)