Quick question antiderivative of e^x^2

[meee]

my retarded textbook has this question i need the antiderivate of e^xsquared

and i hav no idea. thanks

ps. should this be in the calculus forum?

i don't really know what calc is?

 

[benorin]

The antiderivative of $$e^{x^2}$$ cannot be expressed using a finite number of elementary functions, however one may use power series to arrive some sort of an answer, as in:

$$\int e^{x^2}dx = \int \sum_{n=0}^{\infty}\frac{x^{2n}}{n!} dx = \sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)n!}+C$$​

hence $$\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)n!}+C$$ is the most general antiderivative of $$e^{x^2}$$.

Re: P.S.: If you are asking about anything involving limiting processes such as limits, derivatives, antiderivatives (a.k.a. integrals), etc., that would be calculus (excepting perhaps so-called "end-behavior" of functions which arise in some precalc courses). Hence your question about an antiderivative should indeed be posted in the calculus forum.

 

[meee]

ok geeez thanks! i didnt think it would be that.. complex , hehe thanks! and now i know what calculus is

 

[Data]

Also, be careful with exponential notation. e^x^2 is ambiguous because exponentiation is not associative. It could mean

$$e^{x^2}$$

OR

$$(e^x)^2$$,

which are completely different.

 

[VietDao29]

Also, be careful with exponential notation. e^x^2 is ambiguous because exponentiation is not associative. It could mean

$$e^{x^2}$$

OR

$$(e^x)^2$$,

which are completely different.

Unlike other operations, exponents are evaluated from Right to Left. i.e, if one writes $$a ^ {b ^ c}$$, it can be taken for granted that it's the same as writing: $$a ^ {\left( b ^ c \right)}$$
Other wise, it should be written:
$${\left( a ^ b \right)} ^ c$$
See Special Cases in Order of Operations. :)

 

[benorin]

yet the terminology e^xsquared was clear, no?

 

[BobG]

yet the terminology e^xsquared was clear, no?

No. Considering how you asked the question, I would have assumed you meant:

$$\int{(e^x)^2}dx$$

which can be solved by u-substitution.

 

[hello12345]

No. Considering how you asked the question, I would have assumed you meant:

$$\int{(e^x)^2}dx$$

which can be solved by u-substitution.

if you are referring to this question, think really hard back to indices laws x^2*x^3=x^5 ( when you multiply you add ) (e^x)^2 =(e^x)(e^x)=(e^2x)

Anti D = (1/k)*(e^2x)+c ( note 2 is K )
(1/2)*(e^2x)+c