NCERT Class 12 · Ch 7 Exercise 7.4 · Q5
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.4 Question 5
Evaluate \(\int \frac{3 x}{2 x^{4} + 1}\, dx\).
💡 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: \(\frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} \right)}}{4}\) + C.
- Work on each open interval where the integrand is real and defined.
- u=√2x²; du=2√2x dx.
- An antiderivative is F(x)=\(\frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x^{2} \right)}}{4}\).
- Differentiate this expression to check that F′(x)=\(\frac{3 x}{2 x^{4} + 1}\). Add an arbitrary constant C on each domain component.
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