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Evaluate
- Thread starter KEYWEST17
- Start date
\(\displaystyle -\cos x\) is an antiderivative of \(\displaystyle \sin x\), and antidifferentiating \(\displaystyle \tan x\) is more complicated.
One way to antidifferentiate \(\displaystyle \tan x\) is to rewrite it in terms of \(\displaystyle \sin x\) and \(\displaystyle \cos x\) and do a u-substitution.
One way to antidifferentiate \(\displaystyle \tan x\) is to rewrite it in terms of \(\displaystyle \sin x\) and \(\displaystyle \cos x\) and do a u-substitution.
The first term is right. The second is not. \(\displaystyle \tan x =\frac{\sin x}{\cos x}\). You still have to antidifferentiate. Let \(\displaystyle u=\cos x\). Then \(\displaystyle du=-\sin x dx\). So the antiderivative of \(\displaystyle \tan x =\frac{\sin x}{\cos x}\) is \(\displaystyle -\ln |u| + C = -\ln |\cos x|+C\)