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Does anyone know how to do this integral? Mapple just thinks and think and never gives an answer. I couldn't find a primitive in a table either.

[tex]\int_{0}^{\pi}\int_{0}^{+\infty}\frac{r^4\sin^3\theta}{(c+br\cos\theta+(\sin^2\theta )r^2)^3}drd\theta[/tex]

In one attempt, I used a table to reduce the r integral to

[tex]\int_{0}^{\pi}\int_0^{+\infty}\frac{\sin^3\theta}{(c+br\cos\theta+(\sin^2\theta) r^2)^3}dr[/tex]

But what's the integral of that?

[tex]\int_{0}^{\pi}\int_{0}^{+\infty}\frac{r^4\sin^3\theta}{(c+br\cos\theta+(\sin^2\theta )r^2)^3}drd\theta[/tex]

In one attempt, I used a table to reduce the r integral to

[tex]\int_{0}^{\pi}\int_0^{+\infty}\frac{\sin^3\theta}{(c+br\cos\theta+(\sin^2\theta) r^2)^3}dr[/tex]

But what's the integral of that?

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