NCERT Class 12 · Ch 7 Exercise 7.2 · Q21
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 21
Evaluate \(\int \tan^{2}{\left(2 x - 3 \right)}\, dx\).
💡 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: \(- x + \frac{\tan{\left(2 x - 3 \right)}}{2}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Use tan²u=sec²u−1 and u=2x−3.
- An antiderivative is F(x)=\(- x + \frac{\tan{\left(2 x - 3 \right)}}{2}\).
- Differentiate this expression to check that F′(x)=\(\tan^{2}{\left(2 x - 3 \right)}\). Add an arbitrary constant C on each domain component.
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