Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #133
Evaluate \(\int \frac{1}{x^{2} + 16}\,dx\). Work on each connected open interval where the real integrand is defined.
✅ Step-by-Step Solution
Final Answer: \(\frac{\operatorname{atan}{\left(\frac{x}{4} \right)}}{4}\) + C
- Let u=x/4, dx=4du. Then I=(1/4)∫du/(1+u²)=(1/4)arctan u+C.
- Therefore the required integral is \(\frac{\operatorname{atan}{\left(\frac{x}{4} \right)}}{4}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let u=x/4, dx=4du. Then I=(1/4)∫du/(1+u²)=(1/4)arctan u+C.
- [0.5 marks] Therefore the required integral is \(\frac{\operatorname{atan}{\left(\frac{x}{4} \right)}}{4}\) + C.
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