# How do you integrate #int (3-x)7^((3-x) ^2)dx#?

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To integrate ( \int (3-x)7^{(3-x)^2}dx ), you can use substitution. Let ( u = 3 - x ). Then, ( du = -dx ). Substituting these into the integral, we get:

[ \int -(3 - u)7^{u^2}du ]

Now, we can rewrite this integral as:

[ -\int (3u - 7^{u^2})du ]

Now, we integrate each term separately:

[ -\left(\frac{3u^2}{2} - \frac{7^{u^2}}{u^2}\right) + C ]

Finally, substitute back ( u = 3 - x ) to get the final answer:

[ -\left(\frac{3(3-x)^2}{2} - \frac{7^{(3-x)^2}}{(3-x)^2}\right) + C ]

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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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