CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Q303 Marksindefinite_integrals
CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Question 30 (Integrals)
Evaluate \(\int\frac{2x+1}{\sqrt{x^2+6x}}\,dx\).
✅ Step-by-Step Solution
Final Answer: 2√(x²+6x)−5 ln |x+3+√(x²+6x)|+C on x<−6 or x>0.
- Split the numerator as (2x+6)−5 and write x²+6x=(x+3)²−9.
- The first part is 2√(x²+6x). For the second use the standard logarithmic primitive of 1/√(u²−9) with u=x+3.
- Combine the two terms, with an independent constant on each real component.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Split the numerator as (2x+6)−5 and write x²+6x=(x+3)²−9.
- [2 marks] The first part is 2√(x²+6x). For the second use the standard logarithmic primitive of 1/√(u²−9) with u=x+3.
- [0.5 marks] Combine the two terms, with an independent constant on each real component.
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