can someone explain this (1 Viewer)

[xeriphic]

sorry for the late reply my internet wasn't working properly

Heinz: after looking at the question again i figured out a way to answer it without the need for substitution, here it is for future reference

int ((x^2)(e^2x^2) - 1) / x dx

= int x(e^2x^2) - 1/x dx

= 1/4 int 4x(e^2x^2) dx - int 1/x dx

= (1/4)(e^2x^2 - ln x) + c

CM_Tutor: i see, apparently i told the teacher the same thing and he said it always need to be in the simplest form, now that you have cleared it up, i feel more comfortable now in case i forget to simplfy it in the future, thanks

thanks everyone for the help

 

[:: ck ::]

oh yeh thx xayma

 

[CM_Tutor]

Originally posted by :: ryan.cck ::
if it was a definite integral wouldnt the answer differ?!

As Xayma said, the answer is no, and the reason is that the answers differ only in their constants. ie:

(1 / 2)ln(2x) + C = (1 / 2)(ln 2 + ln x) + C = (1 / 2)ln x + (1 / 2)ln 2 + C = (1 / 2)ln x + C' where C' = C + (1 / 2)ln 2

 

[xeriphic]

lol i just realised about the constant c as well for it will be different for each