NCERT Class 12 · Ch 7 Exercise 7.1 · Q18
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.1 Question 18
Evaluate \(\int \left(\tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}\, dx\).
💡 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: \(\tan{\left(x \right)} + \sec{\left(x \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Split the integrand into sec²x+sec x tan x; these are derivatives of tan x and sec x.
- An antiderivative is F(x)=\(\tan{\left(x \right)} + \sec{\left(x \right)}\).
- Differentiate this expression to check that F′(x)=\(\left(\tan{\left(x \right)} + \sec{\left(x \right)}\right) \sec{\left(x \right)}\). Add an arbitrary constant C on each domain component.
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