The imageshack link went down so I made a direct attachment.
Made the problem nice and neat with Word Tools: I have a midterm on monday and I can SOLVE ANY problem and have memorized all common trig integrals. This is the only thing I can't do and its frustrating me and I forgot to ask my professor in office hours. Ive done every homework assignment twice, im intent on acing this class, and this is a harder problem on the review for the test.
http://img504.imageshack.us/img504/1460/calc2la2.png
I have tried all sorts of substitutions, even completeing the square and then using trig identities, Ive been working non stop on this problem for 40 minutes..
Could someone please help me, thank you in advance
Another method:
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The first integral is simple: Make the substitution
The second integral is simple if you're familiar with hyperbolic functions but not so simple if you're not:
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It can also be done using a trig substitution but that's a pain.
Note: which would explain why the answer can also be expressed using logarithms:
hmm interesting, we are allowed to leave multiple variables within the integral as long as they cancel?
hmm.. thats not the answer it gives on the website, its expressed in "ln". We are not required to memorize the natural log formulas, but just by speculation I dont think it would equal his answer, but it looks right to me.
interesting I never thought you could have the "dt" and the actual variable differ, man.. all these tricks and stuff
thanks guys,
sorry got clouded in the whole mess you guys posted trying to decipher it
you're guys method was pretty advanced, I dont think I have ever encountered a problem this hard yet, glad I came here for a fast response, well test tomorrow.. learning the reduction formulas for the 10 pts of extra credit, hoping for 130/120 lets hope
Also I prefer trig methods for some reason
Thanks again