integration

IDKKKKKK.......!!!!

You could try using Desmos.com it's a graphing calculator that will give you a visual of that equation. Sometimes it helps.

∫ (sec(x))^2 * (sec(x))^2 dx

Well.....let's write this in another form

∫ (sec(x)^2 * ((tan(x))^2 + 1 ) dx

Let's split this int o two integrals

∫ (sec(x))^2 * (tan(x)^2 dx + ∫ (sec(x))^2 dx

The second one is easy......we'll come back to it!!

In the first integral, let tan(x) = u

Then, du = (sec(x))^2 dx

So we have

∫ u^2 du =

u^3 / 3 + C =

((tan(x))^3 / 3 + C

The second integral just evaluates to tan(x) + C

So, putting this together, and realizing that C + C is just another constant C, we have

((tan(x))^3 / 3 + tan(x) + C

You can check that this is true by taking the derivative of this......after simplifying, you should get (sec(x))^4 = (sec(x))^2 * (sec(x))^2

Hope this helps.....