How can I determine if a given integral is solvable?

[bomba923]

Ok...now how do I know if a certain integral is solv/integrat-able or not?
Just by looking at the inside function, how can I tell if the integral can be solved or not??

 

[dextercioby]

How about these steps:

1.Try conventional methods:part integration,substitutions,partial fraction decompositions,residues theorem.

2.If it doesn't work,then search for it in "Gradsteyn & Rythzik".

3.If it's not there,the primitive/anitderivative exists,but it's not expressible through elementary functions.

Daniel.

 

[Sirus]

The Wolfram Integrator can also be helpful as a quick reference technique.

 

[dextercioby]

Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything...


Daniel.

 

[Zurtex]

Trust me,that one is useless for nasty integrals.I tried it for about 3 times over the last month and it wouldn't give me anything...


Daniel.

Really? Can you give me an example please.

 

[dextercioby]

I tried an integral that comes up in the Laplace Transform of arctangent

\int_{0}^{+\infty} e^{-sx}\arctan x dx

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.

 

[Zurtex]

I tried an integral that comes up in the Laplace Transform of arctangent

\int_{0}^{+\infty} e^{-sx}\arctan x dx

Of course,i asked for the antidifferential,i thought i could apply the theorem of Leibniz & Newton myself...

Daniel.

Works fine for me when I enter:

Exp[-s x] ArcTan[x]

 

[dextercioby]

Thenx,Zurtex,there's no wonder i couldn't do it... I misstyped something...
I like the result,though...

Daniel.

 

[Zurtex]

Thenx,Zurtex,there's no wonder i couldn't do it... I misstyped something...
I like the result,though...

Daniel.

Yeah I can't help thinking Wolfram are trying to introduce their own brand of maths