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Step-by-step Solution

Integral of (y-2)/(y+3)

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Answer

$y+3-5\ln\left|y+3\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{y-2}{y+3}dy$
1

Split the fraction $\frac{y+-2}{y+3}$ in two terms with same denominator

$\int\left(\frac{y}{y+3}+\frac{-2}{y+3}\right)dy$
2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int\frac{y}{y+3}dy+\int\frac{-2}{y+3}dy$

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Answer

$y+3-5\ln\left|y+3\right|+C_0$
$\int\frac{y-2}{y+3}dy$

Main topic:

Integration by substitution

Used formulas:

6. See formulas

Time to solve it:

~ 0.9 seconds