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

The integral from 1 to 2 of ln(x) is 2ln(2)-1

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integral from 1 to 2 of ln(x)

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

2 ln (2) - 1

Decimal

0.38629 \dots

Solution steps

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

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{1}^{2}

= [x ln (x) - \int 1 d x]_{1}^{2}

\int 1 d x = x

= [x ln (x) - x]_{1}^{2}

Compute the boundaries:

2 ln (2) - 1

= 2 ln (2) - 1

\frac{d}{d x} (2 x - 8)

\frac{d ^{2}}{d x ^{2}} (9 cos (2 x))

\frac{d}{d x} (2 sin (3 x) + 1)

x \to 0 lim (\frac{e ^{x^{2}} - 1}{x})

\frac{d}{d x} (34 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

What is the integral from 1 to 2 of ln(x) ?
The integral from 1 to 2 of ln(x) is 2ln(2)-1