What is the integral of (x+2)/(x-3) ?

The integral of (x+2)/(x-3) is 5ln|x-3|+x+C

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integral of (x+2)/(x-3)

\int \frac{x + 2}{x - 3} d x

5 ln ∣ x - 3 ∣ + x + C

Solution steps

\int \frac{x + 2}{x - 3} d x

\frac{x + 2}{x - 3} = \frac{5}{x - 3} + 1

= \int \frac{5}{x - 3} + 1 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 \frac{5}{x - 3} d x + \int 1 d x

\int \frac{5}{x - 3} d x = 5 ln ∣ x - 3 ∣

\int 1 d x = x

= 5 ln ∣ x - 3 ∣ + x

Add a constant to the solution

= 5 ln ∣ x - 3 ∣ + x + C

\int (\frac{5 x ^{2} + x - 4}{x ^{2}}) d x

y = - 2 t^{3}, (- 1, 2)

\frac{\partial}{\partial y} (\frac{3 x y}{x ^{4} + y ^{4}})

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

x, - 2 x + 3, 0, 1.5

What is the integral of (x+2)/(x-3) ?
The integral of (x+2)/(x-3) is 5ln|x-3|+x+C