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Evaluate
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Differentiate w.r.t. x
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\frac{\int \frac{1}{x^{2}}\mathrm{d}x}{1+1}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
-\frac{\frac{1}{x}}{1+1}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}.
-\frac{1}{2x}
Simplify.
-\frac{1}{2x}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.