CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q232 Marksindefinite_integrals
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 23 (Integrals)
Evaluate \(\int (x-4)e^x\,dx/(x-2)^3\).
✅ Step-by-Step Solution
Final Answer: eˣ/(x−2)²+C.
- Try the product eˣ(x−2)⁻².
- Its derivative is eˣ[(x−2)−2]/(x−2)³.
- This matches the integrand, proving the primitive.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Try the product eˣ(x−2)⁻².
- [1 mark] Its derivative is eˣ[(x−2)−2]/(x−2)³.
- [0.5 marks] This matches the integrand, proving the primitive.
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