Hint:
Hi guys, I have to teach a lesson on this tomorrow (trainee teacher, gulp!) and can't figure out this problem.
Integrate:
x^2sec^2xtanx.dx
I can't seem to figure out if there's a way to manipulate this to make integration by parts easier. Any ideas? Would making it x^2sec.secxtanx help at all given that secxtanx integrates to sec x?
Thanks in advance for any help.
Ouch. This - is a long one. You will need to use integration by parts twice - it is painless though - and a substitution in one of your parts:
Using substitution:
Setting up the by parts:
Taking integration by parts on the last integral:
Then (I'm only going to do the last part):
All together now: