[tex]\int \frac{d}{dx}f(x)dx = f(x) + C_x[/tex] [tex]\iint \frac{d^2}{dx^2}f(x)dx^2 = f(x) + xC_x + C_{xx}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int \frac{\partial}{\partial x}f(x,y)dx = f(x,y) + g_x(y)[/tex] [tex]\int \frac{\partial}{\partial y}f(x,y)dy = f(x,y) + g_y(x)[/tex]

[tex]\iint \frac{\partial^2}{\partial x^2}f(x,y)dx^2 = f(x,y) + x g_{x}(y) + g_{xx}(y)[/tex] [tex]\iint \frac{\partial^2}{\partial x \partial y}f(x,y)dxdy = f(x,y) + \int_{y_0}^{y}g_x(y)dy + G_x(y_0) + g_y(x)[/tex] [tex]\iint \frac{\partial^2}{\partial y \partial x}f(x,y)dydx = f(x,y) + \int_{x_0}^{x}g_y(x)dx + G_y(x_0) + g_x(y)[/tex] [tex]\iint \frac{\partial^2}{\partial y^2}f(x,y)dy^2 = f(x,y) + y g_y(x) + g_{yy}(x)[/tex]

I was trying apply the idea of indefinite integral (ie, the antiderivative of a function + a arbitrary constant/function) for all possible cases. You think that all equation above are correct?

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# Indefinte integrals

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