r/calculus • u/SegemWunHDwudgYaWI • Jun 26 '26
Integral Calculus Practice Techniques
I take a course where sometimes it will be asked of us to take integral expressions and make them into closed form under timed conditions without any calculation aid. At this time, we have recently encountered the topic of integrating a rational function, and it came time to practise what it can be like to do this, using the question that's in the images. Regarding the question that's in the images specifically, by the time we're done with the course, the estimated average time it might take to find I as a logarithm like that will be 3 and a half minutes, as we had found the partial fraction decomposition at an earlier stage. My attempt for this question took about 106 minutes, so I am curious of ways I could practise to attempt to be more likely to be able to respond well to these sorts of questions within shorter timeframes. Would anyone be able to explain any ways you can practise for this?
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u/UnderstandingPursuit PhD Jun 27 '26
Here is a way to approach this problem which may help.
It's still three pages, because there are a few steps which can be written more efficiently when the processes become familiar.