# Help with an integral

1. Apr 2, 2004

### MathNerd

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

where a is just an arbitrary constant...

Last edited by a moderator: Apr 2, 2004
2. Apr 2, 2004

Oh my. That is ugly.

What kind of evil person is making you do that?

3. Apr 3, 2004

### 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 [Broken]

Last edited by a moderator: May 1, 2017
4. Apr 3, 2004

### ShawnD

Maple 8 says it cannot be done.

5. Apr 3, 2004

### Zurtex

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 [Broken]

Last edited by a moderator: May 1, 2017
6. Apr 3, 2004

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.

7. Apr 4, 2004

### meister

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

Last edited by a moderator: May 1, 2017
8. Apr 4, 2004

### himanshu121

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

9. Apr 4, 2004