How to find the antiderivative of $\frac{5 x}{x^{2} - 1} d x$ $(5x)/(x^2-1)dx$ ?

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Answer 1 · 2015-03-01T15:50:21

The answer is: $y'=ln|x^2-1|+c$ .

Since

$int(f'(x))/f(x)dx=ln|f(x)|+c$ ,

than:

$int(5x)/(x^2-1)dx=5/2int(2x)/(x^2-1)dx=ln|x^2-1|+c$ .

How to find the antiderivative of (5x)/(x^2-1)dx5xx2−1dx(5x)/(x^2-1)dx?