積分 x^a e^b

$\int xe^{x} \, dx = e^{x} (x – 1)$
$\int xe^{-x} \, dx = -e^{x} (x + 1)$
$\int x^{2}e^{x} \, dx = e^{x} (x^{2} – 2x + 2)$
$\int x^{2}e^{-x} \, dx = -e^{x} (x^{2} + 2x + 2)$
$\int x^{3}e^{x} \, dx = e^{x} (x^{3} – 3x^{2} + 6x – 6)$
$\int x^{3}e^{-x} \, dx = -e^{x} (x^{3} + 3x^{2} + 6x + 6)$

$\int xe^{2x} \, dx = e^{2x} ( \frac{1}{2}x – \frac{1}{4} )$
$\int xe^{-2x} \, dx = -e^{2x} ( \frac{1}{2}x + \frac{1}{4} )$
$\int x^{2}e^{2x} \, dx = e^{2x} ( \frac{1}{2}x^{2} – \frac{1}{2}x + \frac{1}{4} )$
$\int x^{2}e^{-2x} \, dx = -e^{2x} ( \frac{1}{2}x^{2} + \frac{1}{2}x + \frac{1}{4} )$
$\int x^{3}e^{2x} \, dx = e^{x} ( \frac{1}{2}x^{3} – \frac{3}{4}x^{2} + \frac{3}{4}x – \frac{3}{8} )$
$\int x^{3}e^{-2x} \, dx = -e^{x} ( \frac{1}{2}x^{3} + \frac{3}{4}x^{2} + \frac{3}{4}x + \frac{3}{8} )$