another e integration: xe^(-x^2)

x times e to the negative x squared

Question

another e integration:  xe^(-x^2)

x times e to the negative x squared

hartnn · Answer

substitute -x^2 = u 
then du =... ?

jhannybean · Answer

you have two functions, x and e^(something power) you're going to have to use integration by parts :) with u-sub :P I think!!

hartnn · Answer

if you observe, you'll find that integration by parts won't be required! :)

jhannybean · Answer

..I wasn't observing, lmao.

anonymous · Answer

is this the ans>e^-x^2

hartnn · Answer

you are missing some constants only.....

anonymous · Answer

u mean i shoud add a c as constant..........so the actual rslt wold be=
e^-x^2

hartnn · Answer

no , no ...when you put u= -x^2
what did you get du =... ?

anonymous · Answer

oh sorry......i had e litl mistake................du=-2xdx.....so ans is=-1/2e^-x^2

hartnn · Answer

jhannybean is solving for you nicely, confirm your answer with her, and watch! LOL

jhannybean · Answer

$$\huge \int\limits xe^{(-x^2)}dx$$let u = -x^2 du = -2x dx -> du /-2 = xdx$$\huge -\frac12\int\limits e^{(u)}du = -\frac12e^{u}+ c $$$$\huge -\frac12e^{-x^{(2)}}+c$$

jhannybean · Answer

I hope you can read it. ^_^

hartnn · Answer

both of you are absolutely correct! :D

anonymous · Answer

thnx   jhannybean......