Message Boards Message Boards

0
|
4649 Views
|
2 Replies
|
3 Total Likes
View groups...
Share
Share this post:

[?] Use substitution (or other) method to get a specific form integral?

Roberto Rivero
Posted 4 years ago

Hi, from a book need to solve an integral: enter image description here , was handwrite solved, but Mathematica show the answer in different form, with code:

Integrate[x^3 (2 - x^2)^12, x]

and

Integrate[x^3 (2 - x^2)^m, x] /. m-> 12

get this: mathematica-show

but the question is, can get a form that looks like this?:

desire form

which is the answer by handwrite and solution book. Thanks!
POSTED BY: Roberto Rivero
2 Replies
Sort By:

This is sightly different from the method provided by Hans Dolhaine, and slightly different from the desired form, but it might suffice depending on requirements.

jj = Integrate[x^3 (2 - x^2)^12, x];
divisor = x^2 - 2;
pq = PolynomialQuotientRemainder[jj, divisor, x];
Factor[pq[[1]]]*divisor + pq[[2]]

(* Out[3011]= 4096/91 + 1/364 (-2 + x^2)^13 (2 + 13 x^2) *)
POSTED BY: Daniel Lichtblau

Yep. You can get that, but it is somewhat, say, artificial

jj = Integrate[x^3 (2 - x^2)^m, x] /. m -> 12


(jj /. (2 - x^2) -> p /. (2 + 13 x^2) -> q /. 
q -> ((2 - x^2) (PolynomialQuotient[2 + 13 x^2, 2 - x^2, x] + 
PolynomialRemainder[2 + 13 x^2, 2 - x^2, 
x]/(2 - x^2))) /. (2 - x^2) -> p // Expand) /. 
p -> 2 - x^2
POSTED BY: Hans Dolhaine
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract