Question

integral of x³+x+1/x²-1

Answer 1

you should use parentheses for writing proper expressions.

$\frac{x^3+x+1}{x^2-1} = x + \frac{2x+1}{x^2-1}=\\ \\Integrate\ now$

$\int\limits^{}_{} {(x+\frac{3}{2}\frac{1}{x-1}+\frac{1}{2}\frac{1}{x+1}}) \, dx \\ \\= \int\limits^{}_{} {x} \, dx + \frac{3}{2} \int\limits^{}_{} {\frac{1}{x-1}} \, dx + \frac{1}{2}\int\limits^{}_{} {\frac{1}{x+1}} \, dx \\ \\\frac{1}{2}x^2+\frac{3}{2}Ln(x-1)+\frac{1}{2}Ln(x+1)+C$