0
120

# The integral of sec^2(x)

The integral of sec^2(x) is given by:

∫ sec^2(x) dx = tan(x) + C

where C is a constant.

This result can be derived using the following steps:

1. Recall that sec(x) = 1/cos(x), so sec^2(x) = 1/cos^2(x).
2. Use the identity cos^2(x) = 1 – sin^2(x) to rewrite sec^2(x) as follows:

sec^2(x) = 1/(1 – sin^2(x))

1. Use the substitution u = sin(x) to rewrite the integral as follows:

∫ sec^2(x) dx = ∫ 1/(1 – u^2) du

1. Integrate both sides:

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

where C is a constant.