Problem with improper integrals

[cesaruelas]

Homework Statement

∫xe^(-2x)dx from x = 0 to ∞

Homework Equations

-xe^(-2x)/2 - e^(-2x)/4 + C

The Attempt at a Solution

lim b→∞ -x/2e^(2b) - 1/4e^(2b) = 0

wolfram alpha says its 1/4 and I do not know why (it does not show steps)

Can you help me?

 

[ehild]

You did not take the lower limit into account. Substitute x=0 and subtract.

ehild

 

[cesaruelas]

You're right lol I'm dumb... anyway substituting the lower limit I get 3/4 and not 1/4 :/
-(-1/2 - 1/4) = 3/4

 

[cesaruelas]

Thank you

 

[cesaruelas]

just saw my mistake... 1/2 should be zero, that way I do get 1/4... thank you again