∫sec u du
To solve the integral of sec(u) du, we can use a technique called u-substitution
To solve the integral of sec(u) du, we can use a technique called u-substitution.
Let’s set u = sec(u), which means du = sec(u)tan(u) du.
Now, we need to rewrite the integral in terms of u.
∫sec(u) du = ∫u * (sec(u)tan(u) du)
We can simplify this by substituting du = sec(u)tan(u) du:
∫sec(u) du = ∫u du
Integrating u with respect to u, we get:
∫sec(u) du = u^2 / 2
Therefore, the antiderivative of sec(u) du is u^2 / 2 + C, where C is the constant of integration.
Note: It’s important to remember that the integration of sec(u) only holds true if we are working with the principal range of u, which is (-π/2, π/2) + πn. If we are working outside this range, the integral of sec(u) becomes more complex.
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