SMALLINT {x^5}{E^{ - {x^2}}}DX = g\left( x \right){e^{ - {x^2}}} + c\)Let x2 = t\( \Rightarrow \FRAC{1}{2}\smallint {t^2}{e^{ - t}}dt = \frac{1}{2}\left[ { - {t^2}{e^{ - t}} + \smallint 2t{e^{ - t}}dt} \right]\) \( = \frac{{ - {t^2}{e^{ - t}}}}{2} - t{e^{ - t}} - {e^{ - t}}\) Replacing t by x2, then we get\( = \left( { - \frac{{{x^4}}}{2} - {x^2} - 1} \right){e^{ - {x^2}}} + c\) \(g\left( x \right) = - \frac{{{x^4}}}{2} - {x^2} - 1\) \(g\left( { - 1} \right) = - \frac{1}{2} - 1 - 1 = - \frac{5}{2}\)