Integrate sec2x

To integrate sec2x, also written as ∫sec2x dx, and sec 2x, we use the u substitution because the integral of secu is a standard solution in formula books, which we can use.

Let u=2x.

Then, du/dx=2.

We transpose for dx to get an expression in terms of du.

We replace 2x with u and substitute for dx with the previously obtained expression. Now we have a new integration that means the same thing but is simpler to solve.

We recall a standard solution for secx from our formula book.

Hence the integral of sec u is shown above, together with the constant ½ that was behind the integral sign.

We replace u with 2x to give our final answer.