Can this tricky integral be solved in general?

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[itex]\pi[\int \right[ \frac{\sqrt{x^2+1}}{x^4+sin(x)^2}\left]\;dx[/itex]

Is this soluble generally?
 
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hamster143 said:
Probably not.

Taylor series it is then.

It's easy to make into a series of partial fractions.
 
http://www.wolframalpha.com/input/?i=\int+sqrt(x^2%2B1)%2F(x^4%2Bsin(x)^2)+dx+