What is the integral from 1 to 2 of (1/y+2/3) ?

The integral from 1 to 2 of (1/y+2/3) is ln(2)+2/3

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integral from 1 to 2 of (1/y+2/3)

\int_{1}^{2} (\frac{1}{y} + \frac{2}{3}) d y

ln (2) + \frac{2}{3}

Decimal Notation

1.35981 \dots

Solution steps

\int_{1}^{2} \frac{1}{y} + \frac{2}{3} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} \frac{1}{y} d y + \int_{1}^{2} \frac{2}{3} d y

\int_{1}^{2} \frac{1}{y} d y = ln (2)

\int_{1}^{2} \frac{2}{3} d y = \frac{2}{3}

= ln (2) + \frac{2}{3}

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