NCERT Class 12 · Ch 7 Exercise 7.3 · Q9
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 9
Evaluate \(\int \frac{\cos{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx\).
💡 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: \(x - \tan{\left(\frac{x}{2} \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Rewrite as 1−1/(1+cos x)=1−sec²(x/2)/2.
- An antiderivative is F(x)=\(x - \tan{\left(\frac{x}{2} \right)}\).
- Differentiate this expression to check that F′(x)=\(\frac{\cos{\left(x \right)}}{\cos{\left(x \right)} + 1}\). Add an arbitrary constant C on each domain component.
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