# integral di e^(ax^3+bx) Dopo aver trovato l'integrale fare il Sviluppo di Taylor secondo grado X =0

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LOIC CABREL on 30 Jan 2024
Edited: Infinite_king on 5 Feb 2024
integral di e^(ax^3+bx)
Dopo aver trovato l'integrale fare il Sviluppo di Taylor secondo grado X =0
Dyuman Joshi on 30 Jan 2024
Since this seems to be a HW question, show us what you have done.

Infinite_king on 5 Feb 2024
Edited: Infinite_king on 5 Feb 2024
Hi LOIC CABREL,
Risponderò alla domanda in inglese. Utilizza Google Translate per tradurre la risposta nella tua lingua locale.
In MATLAB, you can create a symbolic expression and by using 'int' function you can find out the integral of the symbolic expression.
% creating a symbolic expression.
syms a x
f = a*x^2
f =
% integrating the function.
int(f)
ans =
Similarly, 'taylor' function can be used to calculate the taylor series expansion of the given function.
% creating the symbolic function
syms a b x
f = exp( a * x^3 + b *x)
f =
% calculating taylor series expansion
ts = taylor(f,x,0,'order',3)
ts =
In some cases, the 'int' function cannot calculate the integral of the given function. This is because of any one of the following reasons,
• The antiderivative, F, may not exist in closed form.
• The antiderivative may define an unfamiliar function.
• The antiderivative may exist, but the software can't find it.
• The software could find the antiderivative on a larger computer, but runs out of time or memory on the available machine.
In these cases, one way to approximate the integral is by using the Taylor series to approximate the function and then calculating the integral of this approximate function. ( approximation around some point )
% creating the symbolic function
syms a b x
f = exp( a * x^3 + b *x)
f =
% calculating taylor series expansion
ts = taylor(f,x,0)
ts =
% calculating the antiderivative
int(ts)
ans =