When I type in this integral into Mathematica:(adsbygoogle = window.adsbygoogle || []).push({});

$$\int_1^\infty \int_1^\infty \frac{dxdy}{(x+y^2)^2}$$

using a large number like 10^{20}instead of ∞, Mathematica gives me 0.785398. No matter what large number I use, Mathematica always gives me around that value.

However, doing the integral by hand, I get it diverges. I make the substitution u=x+y^2 and v=y. The Jacobian of the transformation is 1, so I get:

$$\int_1^\infty \int_1^\infty \frac{dxdy}{(x+y^2)^2}=

\int_1^\infty dv \int_2^\infty \frac{du}{u^2}=(\infty-1)(\frac{1}{2})

$$

which is divergent.

Also, I noticed weird behavior by Mathematica too. If I change the exponent ##(x+y^2)^2## to a non-integer like ##(x+y^2)^{2.1}##, then the integral jumps from being zero or very large.

Does anyone know what's going on here?

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# Is mathematica wrong about this integral?

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