This is what I got
$\displaystyle \int(1+\frac{1}{x})^{-2}(\frac{1}{x^2})\,dx=-(x+1)^{-1}+C$
The book says the answer is $\displaystyle (1+\frac{1}{x})^{-1}+C$
Why is my answer wrong?
Thanks
Actually both solutions are the same.
$\displaystyle \left(1+\frac{1}{x}\right)^{-1}+C_1$
$\displaystyle =~ \frac{1}{1+\frac{1}{x}}+C_1$
$\displaystyle =~ \frac{x}{x+1}+C_1$
$\displaystyle =~ \frac{x+1-1}{x+1}+C_1$
$\displaystyle =~ 1+\frac{-1}{x+1}+C_1$
$\displaystyle =~ -\frac{1}{x+1}+C_2$
$\displaystyle =~ -(x+1)^{-1}+C_2$