f(x,y) = 1 + 2xy + lnx
Wouldnt integrating this function with respect to x give x+x^2y+1/x? The book gives x+x^2y+xlnx-x+g(y). Im working with line integrals, and dont get how they came up with that solution.
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g(y) is a constant of integration, and x ln(x) - x is... (well, you're getting the ln(x) <--> 1/x thing the wrong way round!)
The integral of ln x is x ln (x) - x , this is a standard integral. And because taking the derivative of a function of y would give zero, you will need to add this when integrating. You can see this when taking the derivative of your solution.
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