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

The integral from 1 to 2 of (x+3)/(x(x+2)) is 2ln(2)-ln(3)+3*(-ln(2)+ln(3))/2

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

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

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

Decimal

0.89587 \dots

Solution steps

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

Expand

\frac{x + 3}{x ( x + 2 )} : \frac{x}{x ( x + 2 )} + \frac{3}{x ( x + 2 )}

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

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

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

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

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