Question:

By Parts: $\dfrac{x^2}{2} \tan^{-1} x - \dfrac{1}{2} \int \dfrac{x^2}{1+x^2} dx$. [1.5 Marks]
$= \dfrac{x^2+1}{2} \tan^{-1} x - \dfrac{x}{2} + C$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Applying Integration by Parts: 1.5 Marks
Evaluating final integral $= \frac{x^2+1}{2}\tan^{-1} x - \frac{x}{2} + C$: 1.5 Marks