What is the integral from 1 to 2 of 3t-2/t ?

The integral from 1 to 2 of 3t-2/t is 9/2-2ln(2)

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integral from 1 to 2 of 3t-2/t

\int_{1}^{2} 3 t - \frac{2}{t} d t

\frac{9}{2} - 2 ln (2)

Decimal

3.11370 \dots

Solution steps

\int_{1}^{2} 3 t - \frac{2}{t} d t

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} 3 t d t - \int_{1}^{2} \frac{2}{t} d t

\int_{1}^{2} 3 t d t = \frac{9}{2}

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

= \frac{9}{2} - 2 ln (2)

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What is the integral from 1 to 2 of 3t-2/t ?
The integral from 1 to 2 of 3t-2/t is 9/2-2ln(2)