Question

помогите решить неопределенный интеграл
   $\int\limits xe^3^x^+^2 \, dx$

Answer 1

$\int\limits {xe^{3x+2}} \, dx = \int\limits {x} \, d(\frac{e^{3x+2}}{3})=\frac{e^{3x+2}}{3}*x- \int\limits {\frac{e^{3x+2}}{3}} \, dx =\\ =\frac{e^{3x+2}}{3}*x-\frac{1}{3}*\frac{1}{3} \int\limits {e^{3x+2}} \, d(3x+2) =\\ =\frac{e^{3x+2}}{3}*x-\frac{e^{3x+2}}{9}+C=\frac{e^{3x+2}}{3}*[x-\frac{1}{3}]+C$