Question

intigration of tan2x​

Answer 1

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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.

u substitution

Let u=2x.

du/dx

Then, du/dx=2.

Expression for dx.

We transpose for dx to get the above expression.

New integration

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

standard solution for tanx

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

integral of tanu du

Hence, we can integrate tanu.

Final Answer

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