Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #37
Evaluate \(\int \frac{x^{2} + 2}{x + 1}\,dx\). Work on either interval separated by x=−1.
✅ Step-by-Step Solution
Final Answer: \(\frac{x^{2}}{2} - x + 3 \log{\left(\left|{x + 1}\right| \right)}\) + C
- Polynomial division gives (x²+2)/(x+1)=x−1+3/(x+1); integrate termwise.
- Therefore the required integral is \(\frac{x^{2}}{2} - x + 3 \log{\left(\left|{x + 1}\right| \right)}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Polynomial division gives (x²+2)/(x+1)=x−1+3/(x+1); integrate termwise.
- [0.5 marks] Therefore the required integral is \(\frac{x^{2}}{2} - x + 3 \log{\left(\left|{x + 1}\right| \right)}\) + C.
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