How to integrate sec^2(x)?

To integrate sec^2(x), use the formula ∫sec^2(x)dx = tan(x) + C.

To derive this formula, start with the derivative of tan(x):

d/dx tan(x) = sec^2(x)

Integrating both sides with respect to x gives:

∫sec^2(x)dx = tan(x) + C

where C is the constant of integration.

Therefore, to integrate sec^2(x), simply apply the formula and add the constant of integration:

∫sec^2(x)dx = tan(x) + C

For example, to find the integral of sec^2(3x), use the formula:

∫sec^2(3x)dx = tan(3x) + C

It is important to note that this formula only works for sec^2(x) and not for other powers of sec(x). For those cases, different integration techniques must be used.