NCERT Class 12 · Ch 7 Exercise 7.3 · Q16
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 16
Evaluate \(\int \tan^{4}{\left(x \right)}\, dx\).
💡 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: \(x + \frac{\tan^{3}{\left(x \right)}}{3} - \tan{\left(x \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Use tan⁴x=(sec²x−1)tan²x and integrate with u=tan x.
- An antiderivative is F(x)=\(x + \frac{\tan^{3}{\left(x \right)}}{3} - \tan{\left(x \right)}\).
- Differentiate this expression to check that F′(x)=\(\tan^{4}{\left(x \right)}\). Add an arbitrary constant C on each domain component.
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