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How do you integrate e^(x^2)

I have tried it by substitution and by parts

so i let u=(x^2)

du/dx = 2x

dx=(1/2x)du

but x=sqrt(u)

so dx = [1/(2*sqrt(u))]*du

so integral of e^(x^2) dx = (e^u)*[1/(2*sqrt(u))]du

after that i do integration by parts both ways but eventually end up with

(e^u)*[1/(2*sqrt(u))]du = (e^u)*[1/(2*sqrt(u))]du

sorry but i am hopeless with latex

help appreciated

Scroll to see replies

You don't. Inexpressible in terms of elementary functions.
omg i hate algebra...I'm a simple one :p: The earth's Equation:
E = Big Bouncy Ball with a molten chewy centre :p:
MrGreedy
I have tried it by substitution and by parts

so i let u=(x^2)

du/dx = 2x

dx=(1/2x)du

but x=sqrt(u)

so dx = [1/(2*sqrt(u))]*du

so integral of e^(x^2) dx = (e^u)*[1/(2*sqrt(u))]du

after that i do integration by parts both ways but eventually end up with

(e^u)*[1/(2*sqrt(u))]du = (e^u)*[1/(2*sqrt(u))]du

sorry but i am hopeless with latex

help appreciated
Reply 3
Avatar for The Muon
The Muon
2
You can't integrate it. Or at least, not in the normal sense of integration.
Reply 4
Avatar for v-zero
v-zero
14
Facepalm. /thread
Glutamic Acid
You don't. Inexpressible in terms of elementary functions.

Could you make any good approximations? (not OP just curious)
Reply 6
Avatar for MrGreedy
MrGreedy
OP
11
Glutamic Acid
You don't. Inexpressible in terms of elementary functions.

no way!
this is most disturbing
i was sure the question required to integrate e^(x^2)
anyway thanks
manderlay in flames
Could you make any good approximations? (not OP just curious)


Mmm, probably. Use the Taylor series for e^(x^2).
Reply 8
Avatar for NesQuiK.
NesQuiK.
13
MrGreedy
.

1/2*√π erfi(x), where erfi(x) is the imaginary error function. ie cant be integrated
Reply 9
Avatar for Jimny
Jimny
MrGreedy
no way!
this is most disturbing
i was sure the question required to integrate e^(x^2)
anyway thanks


Well, does it want numerical approximation, do you have an interval.
Reply 10
Avatar for MrGreedy
MrGreedy
OP
11
Jimny
Well, does it want numerical approximation, do you have an interval.

no
the question involves finding a full analytical solution of a first order differential equation.
MrGreedy
no
the question involves finding a full analytical solution of a first order differential equation.


what's the full question?
Reply 12
Avatar for JMonkey
JMonkey
3
You can "cheat", but as said it's not integrable. This comes up so often even I've seen it. Check out the Gaussian function and error function.
Reply 13
Avatar for MrGreedy
MrGreedy
OP
11
EierVonSatan
what's the full question?

Find the general solution of the equation
DE.jpg
It looks simple enough to do by recognition as long as you're prepared to fiddle about with it. Notice that there's a lot of terms that look similar, like -t^2 sec^2 x . dx/dt and 2t tan x. Can you somehow write those two as the derivative of one term (w.r.t. t)? What about 4xt^2 e^(2x^2) dx/dt and 2t e^(2x^2)? You're then left with cos x . dx/dt + d/dt(stuff) = -2 sin 2t, which looks easy enough to do.
Reply 15
Avatar for yusufu
yusufu
16
MrGreedy
I have tried it by substitution and by parts

so i let u=(x^2)

du/dx = 2x

dx=(1/2x)du

but x=sqrt(u)

so dx = [1/(2*sqrt(u))]*du

so integral of e^(x^2) dx = (e^u)*[1/(2*sqrt(u))]du

after that i do integration by parts both ways but eventually end up with

(e^u)*[1/(2*sqrt(u))]du = (e^u)*[1/(2*sqrt(u))]du

sorry but i am hopeless with latex

help appreciated

Can do it as you would any other:

∫ex2 dx=ex22x \int e^{x^2} \ dx = \frac{e^{x^2}}{2x}

Can check this by differentiating the RHS. :smile:
yusufu
Can do it as you would any other:

∫ex2 dx=ex22x \int e^{x^2} \ dx = \frac{e^{x^2}}{2x}

Can check this by differentiating the RHS. :smile:

you need to change your sig
yusufu
Can do it as you would any other:

∫ex2 dx=ex22x \int e^{x^2} \ dx = \frac{e^{x^2}}{2x}

Can check this by differentiating the RHS. :smile:

ddx(ex22x)≠ex2\frac{d}{dx} (\frac{e^{x^2}}{2x} ) \neq e^{x^2}
Reply 18
Avatar for yusufu
yusufu
16
matt2k8
ddx(ex22x)≠ex2\frac{d}{dx} (\frac{e^{x^2}}{2x} ) \neq e^{x^2}

What do you mean?

ddxex2=2xex2 \frac{d}{dx} e^{x^2} = 2xe^{x^2}
⇒ddxex22x=ex2\Rightarrow \frac{d}{dx} \frac{e^{x^2}}{2x} = e^{x^2}
:s-smilie:
Reply 19
Avatar for yusufu
yusufu
16
manderlay in flames
you need to change your sig

Which part?

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