# How do you find the antiderivative of #int cos(pit)cos(sin(pit))dt#?

Substituting in:

This is a common integral:

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To find the antiderivative of ∫cos(πt)cos(sin(πt))dt, you can use integration by parts. Let u = cos(sin(πt)) and dv = cos(πt)dt. Then, du = -πsin(πt)sin(sin(πt))dt and v = (1/π)sin(πt). Apply the integration by parts formula:

∫udv = uv - ∫vdu

Substitute the values of u, dv, du, and v into the formula and solve the integral. The antiderivative of the given function is:

(1/π)cos(πt)sin(sin(πt)) + C

where C is the constant of integration.

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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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