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How do you find the indefinite integral of #int (3-x)7^((3-x)^2)#?

Answer 1

Cameron Alexander

See answer below:

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Answer 2

Adam Adkins

To find the indefinite integral of (\int (3-x)7^{(3-x)^2}), you can use substitution. Let (u = 3 - x), then (du = -dx). Substituting this into the integral yields:

(-\int u \cdot 7^{u^2} , du)

This resembles the form of the Gaussian integral. The antiderivative of (7^{u^2}) is not expressible in terms of elementary functions, but it can be represented using the error function ((erf)). Thus, the antiderivative of (-u \cdot 7^{u^2}) involves the error function. The final antiderivative will be:

(-\frac{1}{2\sqrt{\pi}} e^{-u^2} + C)

Substituting back (u = 3 - x) gives the final result:

(-\frac{1}{2\sqrt{\pi}} e^{-(3-x)^2} + C)

Where (C) is the constant of integration.

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Answer from HIX Tutor

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.