What is the integral from 0 to 3 of (x^2-5)/(x+2) ?

The integral from 0 to 3 of (x^2-5)/(x+2) is ln(2)-ln(5)-3/2

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integral from 0 to 3 of (x^2-5)/(x+2)

\int_{0}^{3} \frac{x ^{2} - 5}{x + 2} d x

ln (2) - ln (5) - \frac{3}{2}

Decimal

- 2.41629 \dots

Solution steps

\int_{0}^{3} \frac{x ^{2} - 5}{x + 2} d x

\frac{x ^{2} - 5}{x + 2} = \frac{( x ^{2} - 5 ) ( x - 2 )}{( x ) ^{2} - ( 2 ) ^{2}}

= \int_{0}^{3} \frac{( x ^{2} - 5 ) ( x - 2 )}{x ^{2} - 2 ^{2}} d x

Find undefined (singularity) points:

x = 2

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{2} \frac{( x ^{2} - 5 ) ( x - 2 )}{x ^{2} - 2 ^{2}} d x + \int_{2}^{3} \frac{( x ^{2} - 5 ) ( x - 2 )}{x ^{2} - 2 ^{2}} d x

\int_{0}^{2} \frac{( x ^{2} - 5 ) ( x - 2 )}{x ^{2} - 2 ^{2}} d x = - ln (2) - 2

\int_{2}^{3} \frac{( x ^{2} - 5 ) ( x - 2 )}{x ^{2} - 2 ^{2}} d x = 2 ln (2) - ln (5) + \frac{1}{2}

= - ln (2) - 2 + 2 ln (2) - ln (5) + \frac{1}{2}

Simplify

- ln (2) - 2 + 2 ln (2) - ln (5) + \frac{1}{2} : ln (2) - ln (5) - \frac{3}{2}

= ln (2) - ln (5) - \frac{3}{2}

\int (\frac{x}{1 - x ^{2}}) d x

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\frac{\partial}{\partial x} (4 - x^{2} - 2 y^{2})

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What is the integral from 0 to 3 of (x^2-5)/(x+2) ?
The integral from 0 to 3 of (x^2-5)/(x+2) is ln(2)-ln(5)-3/2