# What is the antiderivative of #(sec(x)^2)(tan(x)^2)/((sec(x)^2-(R^2))# where R is a constant?

We have:

Rewriting the numerator:

We will now perform partial fraction decomposition on the remaining integrand:

So we will use the decomposition:

Then:

Returning to the integral:

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

The antiderivative of (\frac{\sec^2(x) \tan^2(x)}{\sec^2(x) - R^2}) with respect to (x) is:

[\frac{1}{2} \left(\ln\left|\frac{\sec(x) + \tan(x)}{\sec(x) - \tan(x)}\right| - R^2 \ln\left|\sec(x) - R\right| + R^2 \ln\left|\sec(x) + R\right|\right) + C]

where (C) is the constant of integration.

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