Mastering u-substitution to solve the integral of sec(u) du

∫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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