# How do you find the integral of #int cos^n(x)# if m or n is an integer?

See the explanation for one way to do these.

So

Next, use substitution to integrate each term one by one.

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To find the integral of (\int \cos^n(x) , dx) where (n) is a positive integer, you can use the method of reduction formulas. The formula for (n > 1) is:

[ \int \cos^n(x) , dx = \frac{1}{n} \cos^{n-1}(x) \sin(x) + \frac{n-1}{n} \int \cos^{n-2}(x) , dx ]

And for (n = 1):

[ \int \cos(x) , dx = \sin(x) + C ]

Where (C) is the constant of integration. You can repeatedly apply the reduction formula until the integral becomes manageable.

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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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