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

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

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

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

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{4} \frac{1}{u} d u

= \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

y^{^{''}} + 25 y = 4 csc^{2} (5 t)

\frac{\partial}{\partial x} (3 x cos (y))

x \to 0 lim (\frac{1}{cos ( 8 x )})

\frac{d}{d x} (- 11 (4 x^{3} - 11)^{13})

\frac{6 x}{x + 3}

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