Question

Помогите плиз. Интеграл (х^2*е^(3х))

Answer 1

$int x^2cdot e^{3x}, dx=[, u=x^2; ,; du=2x, dx,; dv=e^{3x}, dx,; v=frac{1}{3}e^{3x}, ]=\\=frac{1}{3}x^2e^{3x}-frac{2}{3}int x, e^{3x}, dx=[, u=x; ,du=dx,; dv=e^{3x}dx,; v=frac{1}{3}e^{3x}, ]=\\=frac{1}{3}x^2e^{3x}-frac{2}{3}cdot (frac{1}{3}xe^{3x}-frac{1}{3}int e^{3x}, dx)=\\=frac{2}{3}x^2e^{3x}-frac{2}{9}xe^{3x}+frac{2}{27}e^{3x}+C=frac{2}{27}e^{3x}cdot (9x^2-3x+1)+C$