Home › UP Board Class 12 › Calculus › $\displaystyle\int \tan x\,dx$ equals:
$\displaystyle\int \tan x\,dx$ equals:
A$\log|\sec x| + C$
BBoth B and C
C$-\log|\cos x| + C$
D$\sec^2 x + C$
Answer & Solution
Correct answer: B. Both B and C
$\int \tan x\,dx = \int \dfrac{\sin x}{\cos x}\,dx = -\log|\cos x| + C$ via the substitution $u = \cos x$. Since $\log|\sec x| = -\log|\cos x|$, the two forms in B and C differ only by an arbitrary constant absorbed into $C$, and both are correct.
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