How to integrate tan^2(x)?

To integrate tan^2(x), use the identity 1 + tan^2(x) = sec^2(x) and substitution.

To integrate tan^2(x), we can use the identity 1 + tan^2(x) = sec^2(x). Rearranging this identity, we get tan^2(x) = sec^2(x) - 1.

Now, we can substitute u = cos(x) and du = -sin(x) dx. Using the identity sec^2(x) = 1/cos^2(x), we can rewrite the integral as:

∫tan^2(x) dx = ∫(sec^2(x) - 1) dx
= ∫(1/cos^2(x) - 1) dx
= ∫(1/u^2 - 1) (-du/sin(x))
= ∫(1/u^2 - 1) du
= -1/u - u + C
= -1/cos(x) - cos(x) + C

Therefore, the integral of tan^2(x) is -1/cos(x) - cos(x) + C.