If ∫x5e-x²dx = g(x)e-x² + c, where c is a constant of integration, then g(-1) is equal to:

The correct option is A -5/2
Let x² = t
2xdx = dt ⇒ 1/2 ∫t²e-tdt = 1/2[∫-t²e-t + ∫2te-t] = 1/2(-t²e-t) + (-te-t + ∫1.e-tdt) = -t²e-t/2 - te-t - e-t = (-t²/2 - t - 1)e-t = (-x⁴/2 - x² - 1)e-x² + C
g(x) = -1 - x² - x⁴/2
for k = 0
g(-1) = -1 - 1 - 1/2 = -5/2