<p>Okay, so on our quiz today we were to integrate tan x</p>
<p>and i said that it was
ln (secx) + c</p>
<p>but she said the correct answer is...
-ln (cosx) + c</p>
<p>Arent they the same?? Or am i being really stupid?</p>
<p>-ln(cosx) + C is.. -1/cosx * sinx = tanX</p>
<p>ln(secx) + C is... 1/(1/cosx) * (0(cosx) + sinx / cosx^2) so you have...
(sinx/cosx^2)/(1/cosx)... sinx/cosx... tanx..</p>
<p>So, it's the same thing</p>
<p>But, by definition, the answer is -ln(cosx) + C</p>
<p>The integral of tan(x) dx equals ln|sec(x)| + C. They are the same thing though. I don't know what definition makes it different though. I would just leave it with secant cause of the extra negative sign with cosine.</p>
<p>The defintion is basically what EVERYONE else in the Calculus world go by.</p>
<p>Right, I have no clue what you are talking about. I think I can integrate. It's the same answer regardless.</p>
<p>ln(1/cosX) = ln1 - ln(cosX) = 0 - ln(cosx)</p>