Evaluate
\frac{y\sigma x^{2}}{2}+С\sigma +С_{1}
Differentiate w.r.t. x
xy\sigma
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\int xy\mathrm{d}x\sigma
Find the integral of \int xy\mathrm{d}x using the table of common integrals rule \int a\mathrm{d}\sigma =a\sigma .
\left(\frac{yx^{2}}{2}+С\right)\sigma
Simplify.
\left(\frac{yx^{2}}{2}+С\right)\sigma +С
If F\left(\sigma \right) is an antiderivative of f\left(\sigma \right), then the set of all antiderivatives of f\left(\sigma \right) is given by F\left(\sigma \right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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