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

The integral from 1 to e of ((1+ln(x))^2)/x is 7/3

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

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

\frac{7}{3}

Decimal

2.33333 \dots

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= \frac{7}{3}

What is the integral from 1 to e of ((1+ln(x))^2)/x ?
The integral from 1 to e of ((1+ln(x))^2)/x is 7/3