A problem I'm working on asks me at a certain point to integrate the following:
$$x=2\left(\sin\left(y\right)\right)^2.$$
I've never integrated anything in this form. I can't isolate for $y$ either. Is there some sort of implicit integration technique I should be aware of, to get the indefinite integral of this?
Thanks to the below comments, I was able to isolate y and get
$$\sin^{-1}\left(\sqrt{\left(\frac{x}{2}\right)}\right)=y$$
....which still looks insanely messy to integrate. I imagine I can use a u-substitution or something similar to solve this?
$\endgroup$ 81 Answer
$\begingroup$The question is from a very long time ago, but I can still attempt to provide an answer. Implicit integration is kind of like the topic in differential equations called exact differential equations. It’s pretty much tracing backwards from applying multivariable chain rule on a function of multiple variables. I’d say it’s the closest thing I’ve seen to a concept of “implicit integration”.
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