int(x/(4+2*x^2) dx what is the answer?
(1/4)*ln(2+x^2) or 1/4 *ln(4+2x^2) ?

Question

int(x/(4+2*x^2) dx what is the answer?
(1/4)*ln(2+x^2) or 1/4 *ln(4+2x^2) ?

zarkon · Answer

both  ( if you add your constant)

anonymous · Answer

on text the second is the answer whereas on maple the second is answer
can you please explain it ?

anonymous · Answer

@Zarkon

anonymous · Answer

according to the logic the second should be the answer, also when I tried 
int x/(2*x^2+7*a^2) dx on maple this was the answer (1/4)*ln(2*x^2+7*a^2)

zarkon · Answer

that is because they are both correct ...

$$\frac{1}{4} \ln(4+2x^2)=\frac{1}{4} \ln(2(2+x^2))=\frac{1}{4} \ln(2)+\frac{1}{4} \ln(2+x^2)$$

thus the two answers differ by only a constant

anonymous · Answer

so this difference is trivial?

anonymous · Answer

i mean that can we ignore it? but why?

zarkon · Answer

$$\int\frac{x}{4+2x^2}dx$$

$$=\frac{1}{4} \ln(4+2x^2)+c_1$$

or

$$=\frac{1}{4} \ln(2+x^2)+c_2$$

anonymous · Answer

are both answers same?

zarkon · Answer

yes...once you include the constant of integration

anonymous · Answer

if I am not wrong have you abosorbed ln(2) in c2?

zarkon · Answer

$$\frac{1}{4}\ln(2)$$

anonymous · Answer

yeah

anonymous · Answer

got ittttttttttt

anonymous · Answer

thanks a tonne

zarkon · Answer

yw