NCERT Class 12 · Ch 7 Exercise 7.2 · Q15
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 15
Evaluate \(\int \frac{x}{9 - 4 x^{2}}\, dx\).
💡 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: \(- \frac{\log{\left(\left|{4 x^{2} - 9}\right| \right)}}{8}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=9−4x², du=−8x dx.
- An antiderivative is F(x)=\(- \frac{\log{\left(\left|{4 x^{2} - 9}\right| \right)}}{8}\).
- Differentiate this expression to check that F′(x)=\(\frac{x}{9 - 4 x^{2}}\). Add an arbitrary constant C on each domain component.
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