What is the integral of (x^2-1)/(x^2-4)+a ?

The integral of (x^2-1)/(x^2-4)+a is -3/4 (ln| x/2+1|-ln| x/2-1|)+x+ax+C

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integral of (x^2-1)/(x^2-4)+a

\int \frac{x ^{2} - 1}{x ^{2} - 4} + a d x

- \frac{3}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + x + a x + C

Solution steps

\int \frac{x ^{2} - 1}{x ^{2} - 4} + a 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{x ^{2} - 1}{x ^{2} - 4} d x + \int a d x

\int \frac{x ^{2} - 1}{x ^{2} - 4} d x = - \frac{3}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + x

\int a d x = a x

= - \frac{3}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + x + a x

Add a constant to the solution

= - \frac{3}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + x + a x + C

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

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

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

What is the integral of (x^2-1)/(x^2-4)+a ?
The integral of (x^2-1)/(x^2-4)+a is -3/4 (ln| x/2+1|-ln| x/2-1|)+x+ax+C