What is the integral of (3x-13)/(x^2+3x-10) ?

The integral of (3x-13)/(x^2+3x-10) is -ln|x-2|+4ln|x+5|+C

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integral of (3x-13)/(x^2+3x-10)

\int \frac{3 x - 13}{x ^{2} + 3 x - 10} d x

- ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{3 x - 13}{x ^{2} + 3 x - 10} d x

Take the partial fraction of

\frac{3 x - 13}{x ^{2} + 3 x - 10} : - \frac{1}{x - 2} + \frac{4}{x + 5}

= \int - \frac{1}{x - 2} + \frac{4}{x + 5} 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}{x - 2} d x + \int \frac{4}{x + 5} d x

\int \frac{1}{x - 2} d x = ln ∣ x - 2 ∣

\int \frac{4}{x + 5} d x = 4 ln ∣ x + 5 ∣

= - ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣

Add a constant to the solution

= - ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

(5 x^{3} + 3) (x^{4} - 2 x)

\int \frac{1}{( 4 x ^{2} + 1 ) ^{2}} d x

x^{2} - 4, [- 4, 3]

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

\frac{d}{d x} (ln (1 + 2 x^{2}))

What is the integral of (3x-13)/(x^2+3x-10) ?
The integral of (3x-13)/(x^2+3x-10) is -ln|x-2|+4ln|x+5|+C