Crash when Solve for Integral with 15C

[Albert Chan]

(09-02-2017 08:55 PM)Gerson W. Barbosa Wrote:  BTW, as an attempt to improve the execution time. I did

u=x^3 -> x=u^(1/3)

du/dx=3*x^2 -> dx=du/(3*x^2)

-> Integ(e^x^3 dx, 0, 6) = 1/3*Integ(e^u/u^(2/3), 0, 216)

A better way might be integrate from the right, with x=u^3, dx=3 u^2 du
The transformation produce a nice bell-shaped curve.

e^x^3 is increasing function, and \(\displaystyle{e^{6^3}\over e^{5^3}} = e^{91} ≈ 3.3×10^{39}\), we can do \(\int_5^6 e^{x^3}\,dx\)

Sharp EL-506W, n=100 (Simpson's Rule, 200 points), time ≈ 14 sec.

∫(e^u/u^(2/3)/3, u=125. .. 216) = 5.965307107 × 10⁹¹
∫(e^(6-u³)³×3u², u=0. .. 1)        = 5.963938092 × 10⁹¹