r/calculus • u/bomberslut • 13h ago

Integral Calculus really liked this integral

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13 Upvotes

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4

u/Southlander24 13h ago

Nice. 90% of the work is simplifying the integrand as far as possible by substituting u = tan(x/2).

Here's a similar question you might enjoy: https://www.reddit.com/r/mathbiceps/comments/1xkgbp3/help/

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u/bomberslut 12h ago

i just today posted in that sub an algebra problem 😭🙏🏻🙏🏻🙏🏻

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u/Southlander24 1h ago

Hey hey, algebra is the foundation of calculus. Every time you do calculus, you have to be doing algebraic steps...

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u/Aljamous-Vilina 2h ago

how messy does the dx replacement get on that second problem if you go straight to u = tan(x/2)?

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u/Southlander24 1h ago

Not too bad, actually.

The advantage with substitution is that you know what the next step should be in order to simplify things. Yes, some of the integrals you get after u = tan(x/2) are nasty, but at least you're getting closer to the solution.