What is the integral from 1 to 3 of 4ln(x)-2/x ?

The integral from 1 to 3 of 4ln(x)-2/x is 10ln(3)-8

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integral from 1 to 3 of 4ln(x)-2/x

\int_{1}^{3} 4 ln (x) - \frac{2}{x} d x

10 ln (3) - 8

Decimal Notation

2.98612 \dots

Solution steps

\int_{1}^{3} 4 ln (x) - \frac{2}{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} 4 ln (x) d x - \int_{1}^{3} \frac{2}{x} d x

\int_{1}^{3} 4 ln (x) d x = 4 (3 ln (3) - 2)

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

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

Simplify

4 (3 ln (3) - 2) - 2 ln (3) : 10 ln (3) - 8

= 10 ln (3) - 8

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What is the integral from 1 to 3 of 4ln(x)-2/x ?
The integral from 1 to 3 of 4ln(x)-2/x is 10ln(3)-8