# How do you integrate #sec2x tan2x dx#?

I would write the integral as:

we can see that:

with this in mind I write the integral as:

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To integrate sec^2(x) tan^2(x) dx, you can use the substitution method.

Let u = tan(x), then du = sec^2(x) dx.

The integral becomes:

∫ tan^2(x) sec^2(x) dx = ∫ u^2 du.

Now integrate u^2 with respect to u:

∫ u^2 du = (1/3)u^3 + C.

Substitute back u = tan(x):

(1/3)tan^3(x) + C.

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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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