# How do you find the antiderivative of #int sin^5(3x)cos(3x)dx#?

Integrating using the typical power rule for integration:

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To find the antiderivative of ∫sin^5(3x)cos(3x)dx, you can use the substitution method. Let u = sin(3x), then du = 3cos(3x)dx. This leads to du/3 = cos(3x)dx. Substituting these into the integral, we get ∫u^5 * (du/3) = (1/3) * ∫u^5 du. Now integrate u^5 with respect to u, then substitute back u = sin(3x) to get the final antiderivative.

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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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