Question

$\int_{}^{}\frac{\mathbf{x}^{\mathbf{2}}\mathbf{+ 1}}{\mathbf{x(}\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{1)}}\mathbf{dx =}$

• A. $\log\frac{x^{2} - 1}{x} + c$
• B. $- \log\frac{x^{2} - 1}{x} + c$
• C. $\log\frac{x}{x^{2} + 1} + c$
• D. $- \log\frac{x}{x^{2} + 1} + c$

Answer 1

Answer: (A)

$\log\frac{x^{2} - 1}{x} + c$

Answer 2

$I = \int_{}^{}{\left( \frac{2x}{x^{2} - 1} - \frac{1}{x} \right)dx}$ $\Rightarrow$ $I = \log(x^{2} - 1) - \log x + c$

$\Rightarrow I = \log\frac{x^{2} - 1}{x} + c$.