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Original post by walkingcarcass
MDI, that''s differentiating. Sorry to nitpick but integration is a little different.

Ive tried googling, no luck. ''m wondering if they actually can be integrated perfectly at all.

Are there infinite series defined for the inverse circular and hyperbolic functions?

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A Problem Worthy of Attack
Proves It''s Worth by Fighting Back

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I don''t know if there''s a specific infinite series or anything for them, but if you can differentiate them, would a taylor expansion work well enough?

They have closed form solutions. All trig, hyperbolic, and their inverse functions have closed form derivatives and integrals. I sat down and figured them all out once. If you can do one, you can do all of them. To figure them out you need to know the product rule, the chain rule, integration by parts, and some simple trig and hyperbolic identities. Mathworld has all of them listed out, and more, if you can figure out which entry it is (I don''t remember).

I remember finding the solution for integrating sqrt(Ax2 + Bx + C) between two numbers once, for finding the arc length of a 3D parametric curve. I''ve never had more fun in my life as when I was integrating that.

Memories.

walkingcarcass :
I don''t know what you searched for on google, but I tried "table integrals" and got
http://torte.cs.berkeley.edu:8010/tilu
This site is really cool. You can just enter your integrand and it will look up its antiderivative. It even does definite integrals. The syntax is kinda funny, though. There is no ln, only log (I advocate this) and inverse hyperbolics are written as arcsinh etc... Try it out.

vanillacoke :
You are right, all the trig / hyperbolic functions and their inverses have elementary antiderivatives. Also, the fact that you derived them all by hand is impressive. Anyway, you can''t find a elementery antiderivative for sin (x^2). I bet you $500.

no wise fish would go anywhere without a porpoise - The Mock Turtle

quote:

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Original post by walkingcarcass
MDI, that''s differentiating. Sorry to nitpick but integration is a little different.

Ive tried googling, no luck. ''m wondering if they actually can be integrated perfectly at all.

Are there infinite series defined for the inverse circular and hyperbolic functions?

********


A Problem Worthy of Attack
Proves It''s Worth by Fighting Back

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Sorry, I read my forumla book wrong. The thing is pretty hard to follow in places, especially when pages are missing all over the place due to it being ripped to pieces in my bag :-(

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This is the tale of a Northern Soul, looking to find his way back home

GaulertheGoat: Of course, sin(x) is only elementary because we say it is... I bet you $1000 I can find a taylor expansion for the integral of sin(x^2).

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Original post by vanillacoke
GaulertheGoat: Of course, sin(x) is only elementary because we say it is... I bet you $1000 I can find a taylor expansion for the integral of sin(x^2).

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The term "elementery" has a more or less precise meaning. Ask Dr. Math
http://mathforum.org/library/drmath/view/54593.html
(This is the first thing that came up on google.) Anyways, I don''t think I''ll be taking that bet.

no wise fish would go anywhere without a porpoise - The Mock Turtle

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Original post by walkingcarcass
Can log_e(x) be integrated wrt x?

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The others have already shown you the solution, but I''d also like to point out integrals.com; I''ve found it very useful.

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Original post by walkingcarcass
A Problem Worthy of Attack
Proves It''s Worth by Fighting Back

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There is no apostrophe in "its", the possessive form of "it". "It''s" is a contraction.

ln(x) is easy. I''m still having problems finding the integral of 1 / ln(x) I have a feeling about this one...

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Original post by Zipster
I''m still having problems finding the integral of 1 / ln(x)

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Integrals.com returns "LogIntegral[x]". I suspect there''s no clean solution.