# Compute the integral: int_(-infty)^infty 1/(y^4+1)dy

Compute the integral:
$\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}\frac{1}{{y}^{4}+1}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}y$
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lefeuilleton42
${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{{y}^{4}+1}dy={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{{y}^{4}+2{y}^{2}+1-2{y}^{2}}dy=$
${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{\left({y}^{4}+2{y}^{2}+1\right)-2{y}^{2}}dy={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{\left({y}^{2}+1{\right)}^{2}-2{y}^{2}}dy$
You should find $\frac{\pi }{\sqrt{2}}$
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