Evaluate
\frac{\sin(\phi )\ln(|x|)}{2}+С
Differentiate w.r.t. x
\frac{\sin(\phi )}{2x}
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\frac{\sin(\phi )}{2}\int \frac{1}{x}\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\frac{\sin(\phi )}{2}\ln(|x|)
Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.
\frac{\sin(\phi )\ln(|x|)}{2}
Simplify.
\frac{\sin(\phi )\ln(|x|)}{2}+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.
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