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## Homework Statement

Find the function f(x) such that [itex]f''(x) = \frac{1}{x^2}[/itex], [itex]f(1) = 0[/itex] and [itex]f(e) = 0[/itex]

## Homework Equations

[itex]\int f''(x)\,dx = f'(x) + c[/itex]

[itex]\int f'(x)\,dx = f(x) + cx + C[/itex]

## The Attempt at a Solution

[itex]f''(x)= \frac{1}{x^2}[/itex]

[itex]f'(x)= \int \frac{1}{x^2}\,dx = \frac{-1}{x} + c[/itex]

[itex]f(x) = -\int \frac{1}{x} + c\,dx = -ln(x) + cx + C[/itex]

My problem is that I can get the constants to satisfy one of those requirements in the original problem, but I am having trouble getting it to satisfy both.

Thanks in advance

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