testing ibpdv and ibpu

[salvomic]

(05-12-2015 10:18 PM)Arno K Wrote:  ...
So :simplify(subst('int(sqrt(1-x^2),x,0,1)',x=sin(u))) directly produces nothing but PI/4.
Now I tried int(sqrt(1-x^2),x) to see what the Prime would deliver: the answer is too long to be typed here,containing i and LN aside the first part,
...
I am a bit disappointed...

(05-13-2015 05:14 AM)parisse Wrote:  It should be
assume(u>0); a:=subst('integrate(sqrt(1-x^2),x,0,1)',x=sin(u)); a

thank you Parisse!
iw would be interesting also to have a method to get "step by step" solution, here and for the "integration by parts" functions, but anyway still already this is ok...

Arno,
please, control your CAS Settings: I've in CAS: Exact, "Use √" and Principal checked, Complex not checked (with firmware 6975)
with the integral you should get (½)*ASIN(x)+(½)*x*√(-x^2-1) from 0 to 1, that's π/4 (in Home you gets 0.785398...)

try, and let me know...

Salvo