# How do you evaluate the integral #int tanthetaln(sintheta)#?

I will call the left one Integral 1 and the right one Integral 2.

I will call this rightmost integral Integral 3

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To evaluate the integral ∫ tan(θ) ln(sin(θ)) with respect to θ, you can use integration by parts. Let u = ln(sin(θ)) and dv = tan(θ)dθ. Then, differentiate u to find du and integrate dv to find v. After that, apply the integration by parts formula: ∫ u dv = uv - ∫ v du. Finally, substitute the values of u, v, du, and dv into this 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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