Integral question

[lrdheat]

New version...

Integral from 1 to 2 of (x+1)*(x^2+2*x+2)^(1/3) returns the unevaluated integral in CAS. When using surd, I get a message: temporary replacing surd/nthroot by fractional powers. I then get the unevaluated integral back.

In home, and in plot, I immediately get the numeric equivalent.

Why won't this evaluate in CAS as it is the equivalent of of the integral from 1 to 2 of u^(1/3)*du/2?

[Helge Gabert]

Did this work in the 5447 firmware?

On the HP50g, the definite integral between 1 and 2 returns an exact answer, and INTVX returns the symbolic answer for the indefinite integral without any problems.

Maybe try integration by parts . . .

[lrdheat]

Using int() didn't return an evaluated integral in CAS. Don't know if this evaluated in previous firmware. Embarrassed to say that I don't know how to proceed integrating by parts...prime seems to want it in vector form. In any case, surprised that CAS doesn't work with this example. Home and plot handles it numerically with ease.

[parisse]

I'm fixing it (Xcas will be updated next week). It's not integration by part, it's recognition of a f(u)*u' pattern.

[Tim Wessman]

The last question as to why it doesn't spit out immediately a numerical result is due to the way the cas works. If something can't be evaluated symbolically (as bernard just pointed out in this case) it will return it unevaluated. Doing an approx(<returned_integral>) (the shift ENTER function) will return it as an approximate numerical result. Also, if you have 1. or similar as your limit at the bounds, it will automatically do it as an approximation immediately in 1 step since it has a "non-exact" number in the equation.