Assertion (A): dx x^2 + 2x + 3 = 1 2 ^ -1 ( x+1 2 ) + C . Reason (R): dx x^2 + a^2 = 1…
Mathematics · Class 12 · CBSE — Integrals
Assertion (A): \(\displaystyle\int \dfrac{dx}{x^2 + 2x + 3} = \dfrac{1}{\sqrt{2}} \tan^{-1}\left(\dfrac{x+1}{\sqrt{2}}\right) + C\).
Reason (R): \(\displaystyle\int \dfrac{dx}{x^2 + a^2} = \dfrac{1}{a^2} \tan^{-1}\dfrac{x}{a} + C\).
- Both (A) and (R) are true and (R) is the correct explanation of (A).
- Both (A) and (R) are true but (R) is not the correct explanation of (A).
- (A) is true but (R) is false.
- (A) is false but (R) is true.
Answer
(C) (A) is true but (R) is false.
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