Question

найти: ∫( 5х+1) ln ⁡хdx

Answer 1

$\int (5x+1)lnx dx=\int 5xlnx dx+\int lnx dx = \\ u=lnx; dv=5xdx;\\\\du= \frac{dx}{x} ;v=2.5x^2;\\\\=2.5x^2*lnx-\int2.5x^2*\frac{dx}{x}+\int lnx dx=\\=2.5x^2*lnx-\int2.5xdx+\int lnx dx=\\=2.5x^2*lnx-1.25x^2+\int lnx dx=\\=2.5x^2*lnx-1.25x^2+x(lnx-1)+C$