I was trying to solve the following integral:
$$\int_{-1}^1 \sqrt{1-\frac{x}{(1-x^2)^2}}$$
But when I plugged it in to any online calculator, It said it couldn't find the integral and that it might not exist. Does this integral converge or is it just very hard to evaluate? Furthermore, If it can be evaluated, I would appreciate any help evaluating it. Thanks in advance!
Convergence $ \int_{-1}^1 \sqrt{1-\frac{x}{(1-x^2)^2}}$
calculusdefinite integralsintegration
Best Answer
$\lim_\limits{x\to 1^-}\left(1-\frac{x}{(1-x^2)^2}\right)=-\infty$, so the square root isn’t even defined over the whole interval. And even taking its absolute value wouldn’t help, since it blows up.