Due to the holiday season, all my students had gone to vacation so I have a day off playing facebook and saw this integral. I decided to type this up since I haven’t updated the blog recently.

Solution:

integration by parts,

then apply long division onto the integrand,

Now, here is the hard part of the whole problem. We need to integrate this

Here we need to break it into two integrals,

The first integral, let the substitution

Now the harder one, the second integral,

By partial fraction we have,

Hence the integral becomes,

Therefore,

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