Discussion
An antiderivative of the tangent is
Answer: B
Write the tangent as a quotient and substitute \( u = \cos x \), with \( du = -\sin x\,dx \):
\[ \int \frac{\sin x}{\cos x}dx \;=\; -\int \frac{du}{u} \;=\; -\ln|u| + C \;=\; -\ln|\cos x| + C. \]
The same antiderivative is often written \( \ln|\sec x| + C \), the two differing only by the sign taken inside the logarithm
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