Definite Integration
Integration of rational functions
Grade Class 12
Question:
If $f\left(\frac{1-x}{1+x}\right)=x$ and $g(x)=\int f(x)dx$ then
$g(x)$ is continuous in domain
$g(x)$ is discontinuous at two points in its domain
$\lim_{x \to \infty} g'(x) = -1$
$\int g(x) dx = -\frac{x^2}{2} + (2x+1) \ln\left(\frac{1+x}{e}\right) + C$
Step-by-Step Solution
Key Concept: Function inversion and integration
Find f(x) by substituting t = (1-x)/(1+x), then integrate.
Correct Answer: A,C