Question

Find the anti derivative of f''(x)= x^-2
x>0, f(1)=0, f(2)=0

Answer 1

\[\int\limits \frac{1}{x^2}dx\]
Do you know how to do this?

Answer 2

\[\int\limits x^{-1}dx \\ \\ \]
Apply
\[\int\limits x^n dx=\frac{1}{n+1}x^{n+1}+c\]

Answer 3

\[\int\limits\limits x^{-2}dx\]
Apply
\[\int\limits\limits x^n dx=\frac{1}{n+1}x^{n+1}+c\]
So
\[\int\limits \frac{1}{x^2} \, dx=-\frac{1}{x}+c\]