Integrate $\int \frac{1}{(1-x)(1+x)}dx$ Integrate $$\int \frac{1}{(1-x)(1+x)}dx$$
$$\int \frac{1}{1-x^2}dx$$
$$=\tanh^{-1}(x)+C$$
When I look on Desmos though, this is only part of the answer?

The blue is the function that it is supposed to be, and the red is the derivative of the answer I got. As you can see it's right, but only the red is shaded, the other two blue regions are not. Why is this? How can I fix this? My answer is correct, right?

It looks like you're integrating your function $1/(1-x^2)$ on $[1,2]$. Yet, it's singular at $1$, so any definite integral that goes over $\pm 1$ will not be correct.
