$∫\frac{dx}{x^2+a^2}=\frac{1}{2a}log\left|\frac{x-a}{x+a}\right|+c,$ where c is an arbitrary constant

$∫\frac{dx}{x^2-a^2}=\frac{1}{2a}log\left|\frac{x-a}{x+a}\right|+c,$ where c is an arbitrary constant

$∫\frac{dx}{x^2-a^2}=\frac{1}{2a}log\left|\frac{x+a}{x-a}\right|+c,$ where c is an arbitrary constant

$∫\frac{dx}{x^2+a^2}=\frac{1}{2a}log\left|\frac{x+a}{x-a}\right|+c,$ where c is an arbitrary constant