integral sin^-1x sechx dx

Question

across · Answer

You can't integrate this by analytical methods.

whynot · Answer

i know it is a challenge question :(

mr.math · Answer

I think it can be done using complex analysis. I mean consider x as a complex variable, evaluate the integral and then take the real part of that. Maybe! I'll try to do this and see what I get.

whynot · Answer

alright i am gonna try even though i have no idea how to deal with complex analysis as i am a calc2 student.

mr.math · Answer

Does the integral have limits?

whynot · Answer

no it was just like that

whynot · Answer

actually, i am just gonna ask him (who gave me this)

whynot · Answer

there is a trick behind it i guess.

mathmate · Answer

Have you done Taylor's series?

whynot · Answer

No

mathmate · Answer

If you did, this can be expanded into a Taylor series and integrated term by term.

whynot · Answer

oh ok

mr.math · Answer

It doesn't seem to be working, since the representation of arcsin would be a logarithm function and sech would be represented as an exponential and that just makes it more complicated.

whynot · Answer

alright thankyou for trying though :)

mr.math · Answer

Taylor series would be a good choice if you want to evaluate the integral numerically, (i.e estimate the value of the integral for given boundaries).

mr.math · Answer

http://www.wolframalpha.com/input/?i=integral+arcsinx*sechx+dx

whynot · Answer

so we need limits in order to integrate that

mathmate · Answer

Can you check if the denominator is sech(x) or sec(x)?  (hope you don't feel insulted).

whynot · Answer

sech(x)

mathmate · Answer

Wolfram actually timed out.  It will take someone with a Mathematica licence on her computer to finish the job (if it can).

whynot · Answer

yeah i tried wolfram too

mr.math · Answer

There are methods to estimating values of functions that don't have an anti-derivatives or too difficult to find one.

across · Answer

Trapezoidal rule, usw...

mr.math · Answer

I mean estimating their integrals.

whynot · Answer

hm i think then i should ask my tutor who gave me this

mr.math · Answer

You should. He/She was probably trying to write something that seems complicated and challenging :P

whynot · Answer

yh:)

mr.math · Answer

You should. He/She was probably trying to write something that seems complicated and challenging :P

mr.math · Answer

Good luck! :)

whynot · Answer

thankyou:)