This was a problem posted by someone else.
int x * e^(x^3) dx
does this even work? please explain to me...
2007-10-23 13:06:18 · 3 answers · asked by PeteDawg 2 in Science & Mathematics ➔ Mathematics
No. This integral is not elementary.
Let's try a substitution u = x³, x = u^(1/3)
dx = 1/3*u^(-2/3) du
So we finally get
1/3∫ e^u du/u^(1/3),
which is a nonelementary exponential integral.
More generally, ∫ e^x dx/ x^n is always
nonelementary if n is positive.
2007-10-23 15:29:18 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
∫udv = uv - ∫vdu
u = x⁻¹/3; du = (-x⁻²/3)dx
v = e^x³; dv = e^x³(3x²)dx
uv = e^x³/(3x); ∫vdu = ∫e^x³(-x⁻²/3)dx
I guess it's not like riding a bike. I learned this stuff over 40 years ago and haven't used it in 30! Anyway, the way I started doing it looks like it's going to go recursive.
2007-10-23 16:21:42 · answer #2 · answered by Anonymous · 0⤊ 0⤋
You could try integration by parts, but I can't tell you if it will work or not.
2007-10-23 13:23:21 · answer #3 · answered by Viginti_Tres 3 · 0⤊ 0⤋