# What is #int tan^3(x) sec^4(x/2) dx#?

Although it will create a double angle in the tangent function, the first step in this situation should be to remove the half-angle because double angles are simpler to work with.

When we replace these, we observe that:

Observe the formula for the tangent double angle:

Consequently:

Extending:

dividing and using negative exponents when writing, with the exception of the final one, which is the natural logarithm integral:

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

The integral of ( \int \tan^3(x) \sec^4\left(\frac{x}{2}\right) dx ) is ( \frac{2}{3} \tan^3(x) + C ), where ( C ) is the constant of integration.

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

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