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Q.∫dx(x2+2x+2)(x2+4x+5)\int \dfrac{dx}{(x^2 + 2x + 2)(x^2 + 4x + 5)} equals

a
12tan⁡−1(x+1)−12tan⁡−1(x+2)+C\dfrac{1}{2} \tan^{-1}(x+1) - \dfrac{1}{2} \tan^{-1}(x+2) + C
b
12(tan⁡−1(x+1)−tan⁡−1(x+2))+C\dfrac{1}{2} \left( \tan^{-1}(x+1) - \tan^{-1}(x+2) \right) + C
c
tan⁡−1(x+1)−tan⁡−1(x+2)+C\tan^{-1}(x+1) - \tan^{-1}(x+2) + C
d
12tan⁡−1(x+1)+C\dfrac{1}{2} \tan^{-1}(x+1) + C

Correct Answer: Option B

The correct solution involves applying the fundamental concept to derive the final value step by step...

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