Original post by studos
integral of xe^(2lnx)
that is x3 to be integrated
0.25x^4 + c?
Original post by studos
how exactly
e^(2lnx) is simply x^2 ?
e^(2lnx) is simply x^2 ?
, e and ln are inverse functions.
You know for example that (domain blah blah, shhh) because sqrt(x) and x^2 are inverse functions. So when you apply one to the other you get the argument.
In this case: . In general:
Unparseable latex formula:
\displaystlye e^{\ln f(x)} = f(x)
Original post by studos
ok but can I solve the integral with a method without knowing that e^lnx=lnx?
also, I need proof of e^lnx=lnx
if e^lnx=a, then lna=lnx, so not a=lnx
also, I need proof of e^lnx=lnx
if e^lnx=a, then lna=lnx, so not a=lnx
Who said e^ln x = ln x, we're all saying e^ln x = x
The proof is rather straightforward.
Let y= e^ (lnx)
Taking the natural logarithm on both sides gives
ln y= ln [ e^ (lnx) ] = (ln x) * lne =ln x since lne=1
As such, since ln y=lnx, then y=x= e^ (lnx) (shown)
Hope this helps. Peace.
Let y= e^ (lnx)
Taking the natural logarithm on both sides gives
ln y= ln [ e^ (lnx) ] = (ln x) * lne =ln x since lne=1
As such, since ln y=lnx, then y=x= e^ (lnx) (shown)
Hope this helps. Peace.
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