Unexpected additional value in output of integral

Questions
1

Hi;
In calculating an integral (using both the icon from the Classroom Pallett and the Integrate[] function in Mathematica) , it appears that Mathematica is placing an additional value in the results that is both unexpected and unwanted (see attached for full explanation).

Possibly, there is something that I am not understanding about the Integrate command, so please help me understand what I am doing incorrectly, or why Mathematica is placing the extra value that I don’t seem to need.

Thank you so much,

Mitchell Sandlin

IntegralQuestion.nb (18.1 KB)

2

Strange! No idea.

Look at

Simplify[Integrate[(x^2 - 3 x + 2)/(x + 1), {x, 0, xx}] /. xx -> x,  x > -1] // Expand
3

This simply is because Integrate in this way gives an antiderivative - and an antiderivative is always determined up to some arbitrary constant.

4

Hallo Henrik,

clear, but why - 9 / 2 and not some constant, e.g. like C[1] ?

And for example

Integrate[ (x + 2)/(x + 1), x]

does nothing like that
Gruß Hans

5

And look at this !?

p[n_] := Sum[a[j] x^j, {j, 0, n}]  


Table[(Integrate[p[n]/(1 + x), x] // Expand) /. x -> 0, {n, 0, 15}]

and

Table[(Integrate[p[n]/(1 + x) /. a[n] -> 1, x] // Expand) /.   x -> 0, {n, 0, 15}]
6

I gave the integral to Wolfram|Alpha with step-by-step integration. The constant - 9 / 2 appears out of nowhere in the final result, together with “+constant”. I suppose it comes from the internals of the Risch algorithm, which is far from the way a human would normally do.