URGENT !! how to integrate e^3x^2 ?

[steel]

how to integrate e^3x^2 ?

 

[sagystu]

i'm not very sure as i still need to study my pure math yeti'll try

e^3x^2 =e^2(3X)=e^6x=1/6(e^6x) please do tell me if my answer is true or false ... i pretty sure though

 

[snowbrood]

 

[whatsmyname]

You must know your maths to know that the variable "e" and its powers are not affected by integration/differentiation. You will have to use the products/quotients rules to derive this but I don't have time so i will break it down for you. Your question - what I understood is - is the integration of (e)^3x(squared). Imagine f(x)=3x^2 then your question becomes integration of (e)^f(x). Use this quick method to do this.

Integration of e^f(x) .dx = [e^f(x) / f ' (x) ] + k
Differentiation of e^f(x) = {f ' (x)} X {e^f(x)}
Multiplication by the differential of f(x) for differentiation of e and division by the differential of f(x) for integration of e.

Here, answer will be: [ e^ 3 x square / 6x ] + k ; because the differential of 3x^2 is 6x. Hope that helps