What is the integral from-4 to 2 of (x+5)/(x-3) ?

The integral from-4 to 2 of (x+5)/(x-3) is -8ln(7)+6

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integral from-4 to 2 of (x+5)/(x-3)

\int_{- 4}^{2} \frac{x + 5}{x - 3} d x

- 8 ln (7) + 6

Decimal

- 9.56728 \dots

Solution steps

\int_{- 4}^{2} \frac{x + 5}{x - 3} d x

\frac{x + 5}{x - 3} = \frac{8}{x - 3} + 1

= \int_{- 4}^{2} \frac{8}{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_{- 4}^{2} \frac{8}{x - 3} d x + \int_{- 4}^{2} 1 d x

\int_{- 4}^{2} \frac{8}{x - 3} d x = - 8 ln (7)

\int_{- 4}^{2} 1 d x = 6

= - 8 ln (7) + 6

\int_{- 4}^{3} 12 - x - x^{2} d x

\int_{1}^{2} \frac{1}{x ^{2}} - \frac{1}{x} d x

\int_{0}^{20} \frac{1}{16} x e^{- \frac{x}{4}} d x

\int_{0}^{\frac{1}{2}} 3 y d y

\int_{0}^{2} 3 t t^{2} + 1 d t

What is the integral from-4 to 2 of (x+5)/(x-3) ?
The integral from-4 to 2 of (x+5)/(x-3) is -8ln(7)+6