What is the integral of (-341x+342)/(x^2+x-2) ?

The integral of (-341x+342)/(x^2+x-2) is 1/3 ln|x-1|-1024/3 ln|x+2|+C

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integral of (-341x+342)/(x^2+x-2)

\int \frac{- 341 x + 342}{x ^{2} + x - 2} d x

\frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{- 341 x + 342}{x ^{2} + x - 2} d x

Take the partial fraction of

\frac{- 341 x + 342}{x ^{2} + x - 2} : \frac{1}{3 ( x - 1 )} - \frac{1024}{3 ( x + 2 )}

= \int \frac{1}{3 ( x - 1 )} - \frac{1024}{3 ( x + 2 )} 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{1}{3 ( x - 1 )} d x - \int \frac{1024}{3 ( x + 2 )} d x

\int \frac{1}{3 ( x - 1 )} d x = \frac{1}{3} ln ∣ x - 1 ∣

\int \frac{1024}{3 ( x + 2 )} d x = \frac{1024}{3} ln ∣ x + 2 ∣

= \frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ x - 1 ∣ - \frac{1024}{3} ln ∣ x + 2 ∣ + C

\frac{\partial}{\partial x} (3 x sin (9 x^{2} y))

x \to \infty lim ((1 + x)^{\frac{3}{x}})

\int \frac{1}{x ^{2} + 36} d x

x \to - \infty lim (\frac{x ^{2} + 2}{x ^{3} + x ^{2} - 1})

x \to 0 lim (7 x^{3} + \frac{1}{4} x^{2})

What is the integral of (-341x+342)/(x^2+x-2) ?
The integral of (-341x+342)/(x^2+x-2) is 1/3 ln|x-1|-1024/3 ln|x+2|+C