∫x^2 e^x/2 dx is ... (a) x^2 e^x/2 - 4xe^x/2 - 8e^x/2 + c (b) 2x^2 e^x/2 - 8xe^x/2 - 16e^x/2 + c (c) 2x^2 e^x/2 - 8xe^x/2 + 16e^x/2 + c

Question

\(∫x^2\,e^{\frac{x}{2}}dx\) is ...

(a) x² e^x/2 - 4xe^x/2 - 8e^x/2 + c

(b) 2x² e^x/2 - 8xe^x/2 - 16e^x/2 + c

(c) 2x² e^x/2 - 8xe^x/2 + 16e^x/2 + c

(d) x² (e^x/2/2) - (xe^x/2/4) + (e^x/2/8) + c

Answer 1

(c) 2x² e^x/2 - 8xe^x/2 + 16e^x/2 + c

I = \(∫x^2\,e^{\frac{x}{2}}dx\)

By Bernoullis formula,