NCERT Class 12 · Ch 7 Exercise 7.2 · Q19
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 19
Evaluate \(\int \frac{e^{2 x} - 1}{e^{2 x} + 1}\, dx\).
💡 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: \(- x + \log{\left(e^{2 x} + 1 \right)}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Rewrite as 2e^(2x)/(e^(2x)+1)−1, then u=e^(2x)+1.
- An antiderivative is F(x)=\(- x + \log{\left(e^{2 x} + 1 \right)}\).
- Differentiate this expression to check that F′(x)=\(\frac{e^{2 x} - 1}{e^{2 x} + 1}\). Add an arbitrary constant C on each domain component.
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