Integral of $\sec^2x$
\[\begin{align*} \int \sec^2(x) dx = \boxed{\tan(x) + C}. \end{align*}\] To find the indefinite integral of $\sec^2(x)$, let’s first recall that the derivative of $\tan x$ is \[\begin{align*} \dfrac{d}{dx}(\tan(x)) = \sec^2(x) \end{align*}\] The First Fundamental Theorem of Calculus states that \[\begin{align*} f(x) = \dfrac{d}{dx} \displaystyle\int_a^x f(x) dx. \end{align*}\] In other words, derivatives and integrals are inverse…
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