integral bug in xCas or HP PRIME

[Albert Chan]

(07-31-2020 11:43 AM)robmio Wrote:  Paradoxically the integral is calculated correctly also with "ibpdv(exp(-s*t)*t*ln(t),-exp (-s*t)/s,t)"

I did not know XCas had build-in integration by parts. Thanks !

d(uv) = u dv + v du     → ∫u dv = uv - ∫v du

Note: ibpu()/ibpdv() result had the minus sign *inside* integral, ∫u dv = uv + ∫-v du

Instead of v = exp(-s*t), you can also let dv = exp(-s*t), and let CAS handle scaling.
Or, even better, let u = t*ln(t), and let CAS figure out v.

XCas> f := exp(-s*t)*t*ln(t)
XCas> m := ibpu(f, t*ln(t),t)          // [-t*ln(t)*exp(-s*t)/s , (exp(-s*t)+ln(t)*exp(-s*t))/s]
XCas> F := m[0] + int(m[1],t)       // note the + sign
XCas> simplify(diff(F,t) - f)            // 0