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

The integral from 1 to e of (2+ln(x))/x is 5/2

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

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

\frac{5}{2}

Decimal Notation

2.5

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{5}{2}

= \frac{5}{2}

\int_{1}^{x} ln (1 + t^{2}) d t

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

\int_{0}^{1} x 5^{x} d x

\int_{0}^{\infty} x λ e^{- λ x} d x

\int_{1}^{5} \frac{1}{x - 1} d x

What is the integral from 1 to e of (2+ln(x))/x ?
The integral from 1 to e of (2+ln(x))/x is 5/2