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Need some tips on solving integration!

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The final exam is going to give you one or two questions on every major technique, they will look similar to problems on the midterm.

I.e. one integration by parts, one partial fractions, one trig substitution, one improper integral, with trig identities and u substitutions mixed in.
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What methods did you learn? There are some 'typical' strategies and then there are some much more difficult ones.
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The trick is realizing there aren't that many things to try (simplify, sub, by-parts, rational functions pipeline). It sounds a little like you expect to know what to do in each case. That's not how it works. You're right. Integration is hard. You just have to try stuff. Then try more stuff. The times when to use the different approaches look kinda the same tbh. You will not know what the first step is. That's, uh, the fun.

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