Question

Evaluate the integral.

integral of t sinh mt dt

Answer 1

Are you familiar with integration by parts? That is what is needed here.

Answer 2

Yes, we understand the concept, but I'm not sure where to begin as every other problem we have dealt with only uses two terms, and this one has three.
Any suggestions?

Answer 3

Certainly :D

I would define your terms as follows, just ignoring the m and understanding that it is simply a value.

u=x
du=dx
dv=sinh(mx)dx
v=cosh(mx)/m

make sense?
try working with this and let me know if you get stuck :)

Answer 4

haha and i apologize i used x instead of t, just a convenience i do because t looks like a + sign on paper xD

Answer 5

x as a variable just seems to work much better than anything else. We'll let you know if we get stuck. Thanks for the help.

Answer 6

not a problem :D good luck!

Answer 7

How does the dv work into this problem?

Answer 8

\[\int\limits_{}^{}udv=uv-\int\limits_{}^{}vdu\]

Answer 9

So truthfully, it's not used specifically in finding anything, but it's what you take the integral of in order to get your v :D

Answer 10

I'm gonna go aid some other people so i'll leave the answer i got here. If you find anything inconsistent, just give a holler :)

\[\int\limits_{}^{}tsinh(mt)dt= \frac{ mtcosh(mt)-\sinh(mt) }{ m ^{2} }+c\]

Answer 11

Thank you very much!

Answer 12

We ended up getting the same answer as you, so thank you yet again.

Answer 13

haha glad it worked :D