# How do you integrate #int x^c e^(x^d)dx#, where #c>d#, using integration by parts?

Use the recurrence formula

with initial

Making a call right now

with

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To integrate ( \int x^c e^{x^d} , dx ) where ( c > d ) using integration by parts, we let:

( u = x^c ) and ( dv = e^{x^d} , dx ).

Then, we find:

( du = cx^{c-1} , dx ) and ( v = \int e^{x^d} , dx ).

Since ( v ) does not have a simple antiderivative, we cannot directly integrate it. Therefore, integration by parts would not be applicable in this case.

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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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