# what is this integralWatch

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#1
integral of xe^(2lnx)
0
3 years ago
#2
(Original post by studos)
integral of xe^(2lnx)
that is x3 to be integrated
0
3 years ago
#3
0.25x^4 + c?
0
3 years ago
#4
e^(2lnx) is simply x^2, so to integrate that function will simply boil down to determining the integral of x^3, which is obvious.
0
#5
how exactly
e^(2lnx) is simply x^2 ?
0
3 years ago
#6
(Original post by studos)
how exactly
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: 0
#7
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
0
3 years ago
#8
(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
Who said e^ln x = ln x, we're all saying e^ln x = x
0
3 years ago
#9
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.
0
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