\int \frac{dx}{(x^2+a^2)^2}  \\=   \frac{1}{a^2}  \int \frac{a^2+x^2-x^2} {(x^2+a^2)^2} \\= \frac{1}{a^2} \int \frac{dx}{x^2+a^2} - \frac{1}{a^2}\int \frac{x^2}{(x^2+a^2)^2} dx  = \\
\frac{1}{a^3} \arctan\frac {x}{a} + \frac{1}{a^2} \int \frac {x*x}{(x^2+a^2)^2} dx = \\
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Smjena:
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u=x \\
du=dx
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dV = \frac {x}{(x^2+a^2)^2} dx  \\
V= \int \frac {x}{(x^2+a^2)^2} dx