NCERT Class 12 · Ch 7 Exercise 7.2 · Q18
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 18
Evaluate \(\int \frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}\, dx\).
💡 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: \(e^{\operatorname{atan}{\left(x \right)}}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=tan⁻¹x, du=dx/(1+x²).
- An antiderivative is F(x)=\(e^{\operatorname{atan}{\left(x \right)}}\).
- Differentiate this expression to check that F′(x)=\(\frac{e^{\operatorname{atan}{\left(x \right)}}}{x^{2} + 1}\). Add an arbitrary constant C on each domain component.
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