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

The integral from 1 to e of ((3+ln(x))^3)/x is 175/4

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

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

\frac{175}{4}

Decimal

43.75

Solution steps

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

Apply u-substitution

= \int_{3}^{4} u^{3} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{175}{4}

= \frac{175}{4}

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

\int_{0}^{π} (x) cos (n x) d x

\int_{1}^{4} 1 + x^{2} d x

\int_{2}^{3} 2 d x

\int_{0}^{3} (4 - x) d x

What is the integral from 1 to e of ((3+ln(x))^3)/x ?
The integral from 1 to e of ((3+ln(x))^3)/x is 175/4