# How do you find the antiderivative of #cos(x) Ln(sin(x)) #?

Use substitution and parts.

This can be integrated using parts

Reverse the substitution to finish with

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To find the antiderivative of cos(x) ln(sin(x)), you can use integration by parts. Let u = ln(sin(x)) and dv = cos(x) dx. Then differentiate u and integrate dv to find du and v respectively. Apply the integration by parts formula: ∫u dv = uv - ∫v du. Finally, substitute the values of u, v, dv, and du into the integration by parts formula and evaluate the integral.

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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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