Mastering Integration Techniques | How to Find the Indefinite Integral of sec(x) with Simple Substitution

∫(secx)dx

To find the integral of sec(x) with respect to x, we can use a method called integration by substitution

To find the integral of sec(x) with respect to x, we can use a method called integration by substitution. The first step is to identify a suitable substitution:

Let’s set u = tan(x) + sec(x). Then, calculating du/dx:

du/dx = sec^2(x) + sec(x)tan(x).

Rearranging this equation, we have:

du = (sec^2(x) + sec(x)tan(x)) dx.

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

∫(sec(x)) dx = ∫(sec^2(x) + sec(x)tan(x)) dx.

Using our substitution, sec(x)dx = du, and sec^2(x) + sec(x)tan(x) dx = du. Our integral then becomes:

∫ du.

The integral of du is simply u + C, where C is the constant of integration. Substituting back in for u, we get:

∫(sec(x)) dx = tan(x) + sec(x) + C.

So, the indefinite integral of sec(x) with respect to x is equal to tan(x) + sec(x) + C, where C represents the constant of integration.

More Answers: