x^2*e^(x^2)
1 / | | / 2\ | 2 \x / | x *e dx | / 0
Integral(x^2*E^(x^2), (x, 0, 1))
Use integration by parts:
Let and let .
Then .
To find :
ErfRule(a=1, b=0, c=0, context=exp(x**2), symbol=x)
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | / / 2\ \ | / 2\ | 2 \x / | ____ 2 | 2 \x / ____ |erfi(x) x *erfi(x) x*e | \/ pi *x *erfi(x) | x *e dx = C - \/ pi *|------- + ---------- - --------| + ----------------- | | 4 2 ____| 2 / \ 2*\/ pi /
____ e \/ pi *erfi(1) - - -------------- 2 4
=
____ e \/ pi *erfi(1) - - -------------- 2 4
Use the examples entering the upper and lower limits of integration.