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$\Large\int x^3 e^{x^2} dx=$ \[(a)\;x^2(e^{x^2}-1) \qquad (b)\;\frac{1}{2}x^2(e^{x^2}-1)\qquad(c)\;\frac{1}{2}e^{x^2}(x^2-1) \qquad(d)\;\frac{1}{2}(e^x-1)\]

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