allery$\int \sec^2 x\,dx$ equals
A$\cot x+C$
B$-\cot x+C$
C$\sec x+C$
D$\tan x+C$
Answer & Solution
Correct answer: D. $\tan x+C$
1. We need a function whose derivative is $\sec^2 x$.
2. Since $\dfrac{d}{dx}(\tan x)=\sec^2 x$, we get $\int \sec^2 x\,dx=\tan x+C$.
3. Note $\int \operatorname{cosec}^2 x\,dx=-\cot x+C$, which is option B, a distractor.
_Source: syllabus Mathematics Ch 7 "Integrals", p.289_
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