Integrate tan2x

To integrate tan2x, also written as ∫tan2x dx, and tan 2x, we use the u substitution because the integral of tanu is a standard solution in formula books.

Let u=2x.

Then, du/dx=2.

We transpose for dx to get the above expression.

Hence, our new integration can be writtin in terms of u and is simpler to solve.

Integration of tan x is a standard solution in formula books, as shown above.

Hence, we can integrate tanu.

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