Integral Fail

[Albert Chan]

(08-14-2020 03:44 AM)lrdheat Wrote:  The Prime and CASIO Classpad 2 both fail to integrate the indefinite integral
(3 NROOT x^2 -2*x + 1)^4

The NSpire is successful, produces (3*(x-1)^(11/3))/11

Any guidance on how to enter the integral differently so that the Prime can handle it?

However, the "successsful" result were wrong.

f(x) = |x-1| ^ (8/3)

If x ≥ 1, F(x) - F(1) =   3/11 * |x-1|^(11/3)
If x < 1, F(x) - F(1) = −3/11 * |x-1|^(11/3)

→ F(x) = 3/11 * (x-1) * |x-1|^(8/3) + C

XCas> F := int(abs(x-1)^(8/3),x)
XCas> F := factor(F)

→ \(\large \frac{3 \left(x-1\right)^{3} \left(\left((x-1) \mathrm{sign}\left(x-1\right)\right)^{\frac{1}{3}}\right)^{2}}{11}\)