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

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

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

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Apply u-substitution

: \int_{0}^{1} u^{3} d u

= \int_{0}^{1} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{0}^{1}

= [\frac{u ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= \frac{1}{4}

\int_{0}^{π} (2 x - 1) cos (5 x) d x

\int_{2}^{3} \frac{1}{2 x ^{2} + 3 x - 2} d x

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

\int_{0}^{2} (3 x^{2}) d x

\int_{1}^{2} x^{3} - 3 x^{2} + 2 x d x

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