Delbrøkoppspalting og integrasjon 

 

Delbrøkoppspalting og Integrasjon 

> f:=(x^3+3)/((x^2+1)*(x-4)):
 

> DelbrøkOppspalting(f,x);
 

`/`(`*`(`+`(`*`(`^`(x, 3)), 3)), `*`(`+`(`*`(`^`(x, 2)), 1), `*`(`+`(x, `-`(4))))) = `+`(1, `/`(`*`(`/`(1, 17), `*`(`+`(x, `-`(13)))), `*`(`+`(`*`(`^`(x, 2)), 1))), `/`(`*`(`/`(67, 17)), `*`(`+`(x, `-...
 

> map(Int,%,x);
 

Int(`/`(`*`(`+`(`*`(`^`(x, 3)), 3)), `*`(`+`(`*`(`^`(x, 2)), 1), `*`(`+`(x, `-`(4))))), x) = Int(`+`(1, `/`(`*`(`/`(1, 17), `*`(`+`(x, `-`(13)))), `*`(`+`(`*`(`^`(x, 2)), 1))), `/`(`*`(`/`(67, 17)), `...
 

> lhs(%)=value(rhs(%))+C;
 

Int(`/`(`*`(`+`(`*`(`^`(x, 3)), 3)), `*`(`+`(`*`(`^`(x, 2)), 1), `*`(`+`(x, `-`(4))))), x) = `+`(x, `*`(`/`(1, 34), `*`(ln(`+`(`*`(`^`(x, 2)), 1)))), `-`(`*`(`/`(13, 17), `*`(arctan(x)))), `*`(`/`(67,...