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Should I add a constant $C$ in this step?

$$\begin{align*} \int \left(\sec^2x \, dx - \sec x \tan x \, dx\right) &= \tan x - \int \sec x \tan x \, dx\\\\ \int \left(\sec^2x \, dx - \sec x \tan x \, dx\right) &= \tan x + C - \int \sec x \tan x \, dx \end{align*}$$

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  • $\begingroup$ Just add a constant when you are finished. $\endgroup$ Sep 17 '13 at 3:02
  • $\begingroup$ You can see here how I edited your question. Please see here for a guide to writing math with MathJax, and see here for a guide to formatting posts with Markdown. $\endgroup$ Sep 17 '13 at 3:06
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It is okay not to add one at this step: the remaining integral on the right hand side already creates an arbitrary constant of integration... and the sum of two arbitrary constants is just another arbitrary constant!

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You dont really need to add one, just add one at the very end

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    $\begingroup$ A day late and a dollar short. The dollar: consider $e^{\int\! f(x)\,dx}$ $\endgroup$
    – dfeuer
    Sep 17 '13 at 3:05
  • $\begingroup$ wait... what does that mean $\endgroup$
    – YYC
    Sep 17 '13 at 3:10
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    $\begingroup$ The "wait till the end" is context-dependent. Sometimes it's okay, and sometimes it's not. It depends on what happens to the result of the integration on the way to a final answer. Leaving the constant of integration out until too late in the game is a common student error, so be wary of it when advising a student. $\endgroup$
    – dfeuer
    Sep 17 '13 at 3:19

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