Solving the Integral of ∫ sec(x)tan(x) dx using the Substitution Method

∫ secxtanx dx

To integrate ∫ sec(x)tan(x) dx, we can solve it by using a substitution method

To integrate ∫ sec(x)tan(x) dx, we can solve it by using a substitution method.

Let’s start by letting u = sec(x). This means that du/dx = sec(x)tan(x), and we can express tan(x) dx as (1/sec(x)) du.

Now, let’s substitute these values into our original integral:

∫ sec(x)tan(x) dx = ∫ (sec(x))(sec(x)tan(x)) dx
= ∫ u(1/u) du
= ∫ du
= u + C

Here, C represents the constant of integration.

Remember that we let u = sec(x), so we can replace u with sec(x) in our final result:

∫ sec(x)tan(x) dx = sec(x) + C

Therefore, the result of the integral is sec(x) + C.

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