Integral Help: Simplifying Integration with an Arbitrary Constant

[MathNerd]

Could someone please help me integrate

$$\int \frac { dx } { ( a + x )^2 + sin^{2} ( \pi x ) }$$

where a is just an arbitrary constant...

Thanks in advance...

 

[cookiemonster]

Oh my. That is ugly.

What kind of evil person is making you do that?

cookiemonster

 

[meister]

The Integrator can't do it, therefore it's impossible. (I know this isn't true, but when Mathematica can't do it I get kind of scared.)

http://integrals.wolfram.com/index.en.cgi

It just spits this out: http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&expr=1/Sqrt%5B%28a%2Bx%29%5E2%20%2B%20%28Sin%5BPi%2Ax%5D%29%5E2%5D

 

[ShawnD]

Maple 8 says it cannot be done.
No answer I guess.

 

[Zurtex]

The Integrator can't do it, therefore it's impossible. (I know this isn't true, but when Mathematica can't do it I get kind of scared.)

I can never get that to do a difficult integration when I have one. But yes this does look like a really nasty one.

Edit: I put it in and got this: http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&x=24&expr=1%20/%20%28%20%28a%20%2B%20x%29%5E2%20%2B%20sin%5E2%28%28Pi%29x%29%20%29&y=21

 

[cookiemonster]

Both my version of Mathematica and the Integrator return the integral.

The first one you had, MathNerd, Mathematica could do, but this new one doesn't work out.

cookiemonster

 

[meister]

I can never get that to do a difficult integration when I have one. But yes this does look like a really nasty one.

Edit: I put it in and got this: http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&x=24&expr=1%20/%20%28%20%28a%20%2B%20x%29%5E2%20%2B%20sin%5E2%28%28Pi%29x%29%20%29&y=21

How do you get a sin^2 with no argument?

 

[himanshu121]

U can calculate for certain sets of values of x where sin(pi x)=0 or 1

 

[cookiemonster]

Yeah, really. The integral of a constant is a piece of cake.

cookiemonster