SF9

From Exampleproblems

$\int_0^\infty \sqrt{y} e^{-y^3} dy\,$

Let $z = y^3, dz=3y^2dy=3z^\frac{2}{3}dy\,$

$\frac{1}{3}\int_0^\infty z^\frac{1}{6} e^{-z}z^\frac{-2}{3}dz = \frac{1}{3}\int_0^\infty z^ {-\frac{1}{2}}e^{-z}dz = \frac{1}{3}\Gamma(1/2) = \frac{\sqrt{\pi}}{3}\,$

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SF9

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