I am learning Calculus online and this problem stumped me. The solution doesn't really make sense either. I'm starting to think that the user made a typo. Here is the question to simplify:
$$\frac{d}{dx}\int_{x^2}^1\frac{t^4 + 1}{t^2 + 1}dt$$
if $u = x^2$, then
$\frac{du}{dx} = 2x$, which means $dx = \frac{du}{2x}$ So we have,
$$-\frac{d}{\frac{du}{2x}}\int_1^u\frac{t^4 + 1}{t^2 + 1}dt$$
And then when I simplify it,
$$-\frac{d}{du}\int_1^u\frac{t^4 + 1}{t^2 + 1}*(2x)dt$$
But this still doesn't get rid of the t's. I have no idea how to replace t with x. Also, I am unable to get rid of $dt$, if I could get rid of $dt$ then I would be able to simplify the equation as the derivative of an integral of $f(x)$ is simply $f(x)$