# How do you evaluate the integral of #int tan(x)ln(cosx) dx#?

We can solve this integral using u-substitution, but it is fairly unapparent from the outset.

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To evaluate the integral ∫ tan(x) ln(cos(x)) dx, you can use integration by parts. Let u = ln(cos(x)) and dv = tan(x) dx. Then differentiate u to get du and integrate dv to get v. After that, apply the integration by parts formula:

∫ u dv = uv - ∫ v du

Then, substitute u, v, du, and dv into the formula and integrate accordingly. You may need to use trigonometric identities to simplify the expression during 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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