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$\int x^{2} (ax + b)^{- 2} dx$ is equal to

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2a2x2−balog⁡(ax+b)+C

2a2x2−balog⁡(ax+b)−b2a3(ax+b)+C

2a2x2+balog⁡(ax+b)+b2a3(ax+b)+C

2a2x2+balog⁡(ax+b)−b2a3(ax+b)+C

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detailed solution

Correct option is B

I=∫x2(ax+b)2dxput ax+b=t⇒dx=1adt and x=t−ba∴ I=1a3∫(t−b)2t2dt=1a3∫1+b2t2−2btdt=1a3t−b2t−2blog⁡t+C =1a3ax+b−b2ax+b−2blog⁡(ax+b)+C=2a2x2−balog⁡(ax+b)−b2a3(ax+b)+C

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∫x2(ax+b)−2dx is equal to

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$\int x^{2} (ax + b)^{- 2} dx$ is equal to