Integration recurrence formula (1 Viewer)

[Skeptyks]

So I worked out the recurrence formula for this question for someone else (I had done it before). View attachment 4jay#2oldworlddocument.doc
Answer, however, has a positive 2nd coefficient and negative 3rd, 4th coefficient. Why?

Thanks :]

 

[Aesytic]

when you were finding the integral of cot^6(x), from the first line to the second, the negative sign should also be carried onto the integral of cot^2(x); two negatives make a positive.
you should've had a bracket around -1/3*cot^2(x) - integral cot^2(x), since that whole expression is equal to the integral of cot^4(x), not just the -1/3*cot^2(x)
this means that it should be plus integral cot^2(x) in the second line, and all the other lines of working should change to give the correct answer

 

[Skeptyks]

Ohhh, I'm so stupid haha. Thanks :]]

 

[Carrotsticks]

For this question, tabular IBP would have been easiest, especially for questions asking us to integrate f(x) raised to the power of n (moreso trig functions).

 

[Skeptyks]

For this question, tabular IBP would have been easiest, especially for questions asking us to integrate f(x) raised to the power of n (moreso trig functions).

What is... tabular IBP?

Edit: NVM. Used google and I think it is integration by parts??

 

[Carrotsticks]

Yep, but it is substituted and reduced immediately.