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

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

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

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

\frac{7}{2}

Decimal

3.5

Solution steps

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

Apply u-substitution

: \int_{2}^{5} \frac{u}{3} d u

= \int_{2}^{5} \frac{u}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{2}^{5} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{2}^{5}

= \frac{1}{3} [\frac{u ^{2}}{2}]_{2}^{5}

Compute the boundaries:

\frac{21}{2}

= \frac{1}{3} \cdot \frac{21}{2}

Simplify

= \frac{7}{2}

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