How do you integrate #int x^2e^x dx # using integration by parts?

1 Answer
Jan 27, 2016

#intx^2e^xdx = x^2e^x - 2xe^x + 2e^x + c#

Explanation:

The integration by parts formula say

#intudv = uv - intvdu#

So, if we pick #u = x^2# and #dv = e^x# so we'll have #du = 2x# and #v = e^x#

#intx^2e^xdx = x^2e^x - int2xe^xdx#

Now we pick #u = x# and #dv = e^x#, so #v = e^x# and #du = 1#

#intx^2e^xdx = x^2e^x - 2(xe^x - inte^xdx)#

This last integral is tabled, so

#intx^2e^xdx = x^2e^x - 2xe^x + 2e^x + c#