# How do you find the derivative of #int xe^(3x^2+1) dx# from 0 to 1?

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To find the derivative of the integral ( \int_0^1 xe^{3x^2 + 1} , dx ), you can use the Leibniz rule for differentiating under the integral sign, also known as the Leibniz integral rule or differentiation under the integral sign. The result is the derivative of the integral with respect to a parameter, in this case, ( x ). After applying this rule, evaluate the resulting expression at the upper limit (1) and subtract the value obtained at the lower limit (0).

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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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