# How do you evaluate the integral #int tan^3theta#?

Use the trigonometric identity:

to get:

For the second integral:

Putting it together:

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To evaluate the integral ∫tan^3(θ)dθ, we can use trigonometric identities and integration by parts. By rewriting tan^3(θ) as (sec^2(θ) - 1)tan(θ), we can separate it into two integrals. Then, using the substitution u = tan(θ), du = sec^2(θ)dθ, we can solve each integral separately. Integrating sec^2(θ) yields tan(θ), and integrating 1 yields θ. Therefore, the integral of tan^3(θ) is equal to (1/2)tan^2(θ) - tan(θ) + θ + 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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