What is the integral from 1 to 3 of (x-3ln(x)) ?

The integral from 1 to 3 of (x-3ln(x)) is -9ln(3)+10

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integral from 1 to 3 of (x-3ln(x))

\int_{1}^{3} (x - 3 ln (x)) d x

- 9 ln (3) + 10

Decimal

0.11248 \dots

Solution steps

\int_{1}^{3} x - 3 ln (x) d x

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}^{3} x d x - \int_{1}^{3} 3 ln (x) d x

\int_{1}^{3} x d x = 4

\int_{1}^{3} 3 ln (x) d x = 3 (3 ln (3) - 2)

= 4 - 3 (3 ln (3) - 2)

Simplify

4 - 3 (3 ln (3) - 2) : - 9 ln (3) + 10

= - 9 ln (3) + 10

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What is the integral from 1 to 3 of (x-3ln(x)) ?
The integral from 1 to 3 of (x-3ln(x)) is -9ln(3)+10