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I'm teaching a Calculus II class and we are covering integration techniques. We've covered $u$-substitution, integration by parts, trig integrals, trigonometric substitutions, partial fractions and integration involving hyperbolic functions. I want to give my students some integrals to do that can be done using as many of these methods as possible. So far, I've come up with $\int\frac{x}{x^2-1}dx$ which can be done using partial fractions, $u$-substitution, trigonometric substitution, and a hyperbolic cosine substitution. I was wondering if anyone had other examples like this. Thanks.

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    this should be a community wiki.2012-09-10
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    Are you asking for an integral which requires all of these different methods to do, or an integral which can be done using any one of the various methods?2012-09-11
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    An integral that can be done using any one of the various methods.2012-09-11

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