لتنشيط الذهن 3

للتذكير فقط، مع الشكر

$\LARGE {\color{Red} (1)\int (2x+3)lnx dx;;u=lnx\rightarrow du=\frac{1}{x}dx} $
${\color{Red} dv=2x+3\rightarrow v=x^{2}+3x}$
${\color{Red} I=(x^{2}+3x)lnx-\int (x^{2}+3x)\frac{1}{x}=(x^{2}+3x)lnx-\frac{x^{2}}{2}+3x+c}$

$\LARGE {\color{DarkBlue} (2)\int (2x-1)e^{2x+3}dx;;u=2x-1\rightarrow du=2dx }$
$ {\color{DarkBlue} dv=e^{2x+3}\rightarrow v=1/2e^{2x+3}} $
${\color{DarkBlue} I=1/2(2x-1)e^{2x+3}-\int e^{2x+3}=(1/2)(2x-1)e^{2x+3}-(1/2)e^{2x+3}+c}$