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

The integral from 1 to e of ((1+ln(x))^3)/x is 15/4

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

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

\frac{15}{4}

Decimal

3.75

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{2}

= [\frac{u ^{4}}{4}]_{1}^{2}

Compute the boundaries:

\frac{15}{4}

= \frac{15}{4}

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What is the integral from 1 to e of ((1+ln(x))^3)/x ?
The integral from 1 to e of ((1+ln(x))^3)/x is 15/4