Answer to Question #155285 in Calculus for Tony

Question

Solve the integral of: x/1 - x^(2) dx

Answer 1

Let's solve this problem

$\int\large\frac{x}{1-x^2}dx$

Substituting $u = 1-x^2 \to \large\frac{du}{dx} = -2x(steps) \to dx=-\large\frac{1}{2x}du:$

$= -\frac{1}{2}\int\large\frac{1}{u}du$

Now solving: $\int \large\frac{1}{u}du = ln|u|+C$

Plug in solved integrals: $-\frac{1}{2}\int\large\frac{1}{u}du = -\large\frac{ln|u|}{2}+C$

Substituting back $u = 1-x^2:$ $\int\large\frac{x}{1-x^2}dx = -\large\frac{ln(1-x^2)}{2}+C$

Answer: $-\large\frac{ln(|x^2-1|)}{2} + C$