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

The integral from 1 to 3 of 1+1/u+1/(u^2) is ln(3)+8/3

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integral from 1 to 3 of 1+1/u+1/(u^2)

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

ln (3) + \frac{8}{3}

Decimal Notation

3.76527 \dots

Solution steps

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

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

\int_{1}^{3} 1 d u = 2

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

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

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

Combine the fractions

2 + \frac{2}{3} : \frac{8}{3}

= ln (3) + \frac{8}{3}

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What is the integral from 1 to 3 of 1+1/u+1/(u^2) ?
The integral from 1 to 3 of 1+1/u+1/(u^2) is ln(3)+8/3