NCERT Class 12 · Ch 7 Exercise 7.4 · Q24
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.4 Question 24
Evaluate \(\int \frac{1}{x^{2} + 2 x + 2}\, dx\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: B: \(\operatorname{atan}{\left(x + 1 \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Complete the square (x+1)²+1 and use u=x+1.
- An antiderivative is F(x)=\(\operatorname{atan}{\left(x + 1 \right)}\).
- Differentiate this expression to check that F′(x)=\(\frac{1}{x^{2} + 2 x + 2}\). Add an arbitrary constant C on each domain component.
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