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I have an integral of the form \begin{align*} \left(\int_{0}^{1}\mathrm{exp}(-t^2) \cos t^2 ~dt\right)^{2}. \end{align*} Is there any way to represent it into single integral form?. \begin{align*} \left(\int_{0}^{1}\mathrm{exp}(-t^2) \cos t^2~dt\right)^{2}=\int_{0}^{1}\int_{0}^{1}\mathrm{exp}(-(x^2+t^2)) \cos x^2\cos t^2 ~dxdt. \end{align*}

skorpion
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  • \begin{align} \left(\int_{0}^{1} \exp(-t^{2}) \cos(t^{2}) dt \right)^{2} &= \left(\int_{0}^{1} \exp(-t^{2}) \cos(t^{2}) dt \right) \cdot \left(\int_{0}^{1} \exp(-s^{2}) \cos(s^{2}) ds \right) \ &= \int_{0}^{1} \int_{0}^{1} \exp(-(s^2+t^2)) \cos(s^2) \cos(t^2) ds dt \end{align} – Matthew Cassell Jun 14 '18 at 14:19
  • I mean as a single integral. Its a product which is very simple. Like $\int_{0}^{1} f(x)~dx$ – skorpion Jun 14 '18 at 14:21

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