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Question Number 35043 by math khazana by abdo last updated on 14/May/18

$$lett>0andF\left(t\right)={\int }_0^{\mathrm{\infty }}\frac{sin\left(x^2\right)e^{-{tx}^2}}{x^2}dx$$$$calculate\frac{dF}{dt}\left(t\right).$$

Answered by MJS last updated on 14/May/18

$$F^{\prime }\left(t\right)=-\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\sin \left(x^2\right){\mathrm{e}}^{-x^{2}t}dx$$

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