allery$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals:
A$\tan^{-1} x + C$
B$\sin^{-1} x + C$
C$\log(1+x^2) + C$
D$\dfrac{1}{2}\log(1+x^2) + C$
Answer & Solution
Correct answer: A. $\tan^{-1} x + C$
**Standard form:** $\int \dfrac{1}{a^2 + x^2}\,dx = \dfrac{1}{a}\tan^{-1}(x/a) + C$.
With $a = 1$, this reduces to $\tan^{-1} x + C$.
**Option A would be the integral of $\dfrac{2x}{1+x^2}$, not $\dfrac{1}{1+x^2}$.**
Keep practising Unit 6A: Indefinite Integrals & Fundamental Theorem
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