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

The integral from 1 to e of ((2+ln(x))^3)/x is 65/4

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

\int_{1}^{e} \frac{( 2 + ln ( x ) ) ^{3}}{x} d x

\frac{65}{4}

Decimal Notation

16.25

Solution steps

\int_{1}^{e} \frac{( 2 + ln ( x ) ) ^{3}}{x} d x

Apply u-substitution

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

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

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{2}^{3}

= [\frac{u ^{4}}{4}]_{2}^{3}

Compute the boundaries:

\frac{65}{4}

= \frac{65}{4}

\int_{- 1}^{0} (- x - 1) d x

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\int_{x^{4}}^{x^{5}} (2 t - 1)^{3} d t

What is the integral from 1 to e of ((2+ln(x))^3)/x ?
The integral from 1 to e of ((2+ln(x))^3)/x is 65/4