Hey everyone. This is Andrew Maloney posting with a question:

I can’t figure out what to do with Partial Fractions question 3. I know that my denominator has no Real roots

So it’s a product of one irreducible (over the Reals) quadratic. It seems to me that the partial fractions technique won’t get me anywhere with this problem.

I think I should parse the denominator as:

(x+3)^2 + 25

Then use substitution and trig substitution.

Yes, doing this gives me the answer.

Can anyone see a way that partial fractions could be applied here? In fact, as I move through the other questions, I also can’t find a way to apply the partial fractions technique to question 10. Instead, I use a substitution within a substitution, similar to the technique I used for this problem but with regular substitution instead of trig substitution.

What am I missing?

Thanks!