\( \int xe^{x} \, dx = e^{x} (x – 1) \)
\( \int xe^{-x} \, dx = -e^{x} (x + 1) \)
\( \int x^{2}e^{x} \, dx = e^{x} (x^{2} – 2x + 2) \)
\( \int x^{2}e^{-x} \, dx = -e^{x} (x^{2} + 2x + 2) \)
\( \int x^{3}e^{x} \, dx = e^{x} (x^{3} – 3x^{2} + 6x – 6) \)
\( \int x^{3}e^{-x} \, dx = -e^{x} (x^{3} + 3x^{2} + 6x + 6) \)
\( \)
\( \int xe^{2x} \, dx = e^{2x} ( \frac{1}{2}x – \frac{1}{4} ) \)
\( \int xe^{-2x} \, dx = -e^{2x} ( \frac{1}{2}x + \frac{1}{4} ) \)
\( \int x^{2}e^{2x} \, dx = e^{2x} ( \frac{1}{2}x^{2} – \frac{1}{2}x + \frac{1}{4} ) \)
\( \int x^{2}e^{-2x} \, dx = -e^{2x} ( \frac{1}{2}x^{2} + \frac{1}{2}x + \frac{1}{4} ) \)
\( \int x^{3}e^{2x} \, dx = e^{x} ( \frac{1}{2}x^{3} – \frac{3}{4}x^{2} + \frac{3}{4}x – \frac{3}{8} ) \)
\( \int x^{3}e^{-2x} \, dx = -e^{x} ( \frac{1}{2}x^{3} + \frac{3}{4}x^{2} + \frac{3}{4}x + \frac{3}{8} ) \)