# How do you find the integral of #int (x^2)(e)^(-x^3) dx# from negative infinity to infinity?

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To find the integral of (\int_{-\infty}^{\infty} x^2 e^{-x^3} , dx), you can use the substitution method. Let (u = -x^3), then (du = -3x^2 , dx). Solving for (dx), we get (dx = \frac{-du}{3x^2}). Substituting these into the integral, we get (\int_{-\infty}^{\infty} x^2 e^{-x^3} , dx = \int_{u(-\infty)}^{u(\infty)} \frac{-u}{3} e^{u} , du). Now, integrate (\int \frac{-u}{3} e^{u} , du) using standard techniques. Finally, evaluate the antiderivative from the limits (u(-\infty)) to (u(\infty)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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