# How do you evaluate the integral #int tan^2x/secx#?

We see that:

Splitting up the integral:

Both of these are standard integrals:

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the integral ∫tan^2(x)/sec(x) dx, you can use trigonometric identities to simplify it. Begin by expressing tan^2(x) as sec^2(x) - 1. Then rewrite the integral in terms of sec(x):

∫tan^2(x)/sec(x) dx = ∫(sec^2(x) - 1)sec(x) dx

Now, make a substitution: Let u = sec(x), then du = sec(x)tan(x) dx. Substituting this into the integral, you get:

∫(u^2 - 1) du

Now, integrate term by term:

= ∫u^2 du - ∫1 du = (u^3/3) - (u) + C

Substitute back u = sec(x):

= (sec^3(x)/3) - sec(x) + C

This is the final result for the integral ∫tan^2(x)/sec(x) dx.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7