NCERT Class 12 · Ch 7 Exercise 7.4 · Q16
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.4 Question 16
Evaluate \(\int \frac{4 x + 1}{\sqrt{2 x^{2} + x - 3}}\, dx\).
💡 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: \(2 \sqrt{2 x^{2} + x - 3}\) + C.
- Work on each open interval where the integrand is real and defined.
- The numerator is the derivative of the radicand; substitute it.
- An antiderivative is F(x)=\(2 \sqrt{2 x^{2} + x - 3}\).
- Differentiate this expression to check that F′(x)=\(\frac{4 x + 1}{\sqrt{2 x^{2} + x - 3}}\). Add an arbitrary constant C on each domain component.
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