Q.39. \int \frac{x^2+1}{x(x^2-1)}dx
A. \log x(x^2-1) + c, where c is a constant of integration.
B. \log \left(\frac{x^2-1}{x}\right) + c, where c is a constant of integration.
C. \log (x^2-1) + c, where c is a constant of integration.
D. \log \left(\frac{x^2+1}{x}\right) + c, where c is a constant of integration.
Answer: B
Explanation :-
Let I = \int \frac{x^2+1}{x(x^2-1)}dx
\int \frac{\frac{x^{2}+1}{x^{2}}}{\frac{x^{2}-1}{x}}dxLet t=\frac{x^{2}-1}{x}\Rightarrow dt=\frac{x^{2}+1}{x^{2}}dx
I=\int \frac{1}{t}dt=log(t)+c=log\left ( \frac{x^{2}-1}{x} \right )