How do you find the integral of #(1+ tan^2x)sec^2xdx#?
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To find the integral of (1 + tan^2(x))sec^2(x)dx, you can use trigonometric identities and integration techniques. Start by replacing tan^2(x) with sec^2(x) - 1. Then, integrate term by term. Here are the steps:
- Rewrite the integral as ∫(1 + sec^2(x) - 1)sec^2(x)dx.
- Distribute sec^2(x) to get ∫(sec^2(x) + sec^4(x) - sec^2(x))dx.
- Simplify to get ∫(sec^2(x) + sec^4(x))dx.
- Integrate each term separately: ∫sec^2(x)dx + ∫sec^4(x)dx.
- The integral of sec^2(x) is tan(x) + C, where C is the constant of integration.
- To integrate sec^4(x), use a substitution or integration by parts.
Following these steps, the integral of (1 + tan^2(x))sec^2(x)dx can be evaluated.
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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.
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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