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Re: nasty integrals that Mathematica can't do

> In my research, i've come up with the following integral:
>     Integrate[ CosIntegral[a x] Cos[b x], {x,0,Infinity} ]
> Gradshteyn and Ryzhik have this integral, but apparently, Mathematica
> 3.0.1 can't do it.
> My question: Is there a way to "teach" Mathematica how to do a
> particular type of integral?  Can I somehow plug G+R's solution in
> Mathematica?

You can certaily plug in the solution:


Integrate[ CosIntegral[a_ x] Cos[b_ x], {x,0,Infinity} ]:= GR[a,b]


Now we get

Integrate[ CosIntegral[5 x] Cos[7 x], {x,0,Infinity} ]

GR[5, 7]
Allan Hayes
Training and Consulting
Leicester, UK
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642

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