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Tricky integral

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Looks pretty awful. Can you show the entire problem? (And preferably use more pixels.)
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I’m sorry I don’t remember much about Calc 3, but would a multivariable u-substitution somehow help? I don’t exactly remember how they work, so I’m sorry about that. Just another idea.

Integrating r sec(r^(3) cos(θ)) is tricky. Maybe integration by parts?
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~~Yeah that's pretty gnarly. Have you covered general change of variables yet? Polar doesn't seem too natural for the domain.~~
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Yes, I'd like to see the entire problem too, because I think the integral diverges (as an improper muliple integral).

Along vertical lines x = constant, within a number of entire regions, the integrand has discontinuities that look like 1/y, wherever x\^3 + y\^2.x is an odd multiple of pi/2.
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This integral shouldn't exist, there's plenty of points where x\^3 + y\^2x = pi/2, so that sec(x\^3 + y\^2 x) is undefined. Where is this question from?
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Try looking up a table of trigonometric identities. It’s possible there’s one that makes this easier to integrate.

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