Integral 15lnx dx

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[tex]\int(3x^2 +2x) (x^3 + x^2)^4dx[/tex]
[tex]\int 15 lnx dx[/tex]

[Stancho Pavlov]

[tex]\int15lnxdx=15\int lnxdx[/tex]
[tex]\int lnxdx[/tex] we integrate by parts:
[tex]\int lnxdx = xlnx - \int xdlnx = xlnx - \int x\frac 1 x dx = xlnx - \int dx = xlnx - x = x(lnx - 1)+C[/tex]