Skip to content

Replace arcsec in the table of integrals with equivalent expressions using arccos #114

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
derivitaandrew wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Replace arcsec in the table of integrals with equivalent expressions using arccos #114

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
replace arcsec(x) (which isn't a supported function) with arccos(1/x)… 
… in the table of integrals
  • Loading branch information
@derivitaandrew
derivitaandrew committed Aug 17, 2020
commit acb2877c545b9e2a9f0965c2e0c97abe94ed6aa0
4 changes: 2 additions & 2 deletions .gitattributes
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,3 +1,3 @@
[core]
autocrlf = false

autocrlf=false
12 changes: 6 additions & 6 deletions sources/integral.coffee
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -143,13 +143,13 @@ itab = [
#157
"f(1/sqrt(x^2+a),log(x+sqrt(x^2+a)))",
#158
"f(1/x*1/sqrt(x^2+a),arcsec(x/sqrt(-a))/sqrt(-a),or(not(number(a)),a<0))",
"f(1/x*1/sqrt(x^2+a),arccos(sqrt(-a)/x)/sqrt(-a),or(not(number(a)),a<0))",
#159
"f(1/x*1/sqrt(x^2+a),-1/sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))",
#160
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))",
#161
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arcsec(x/sqrt(-a)),or(not(number(a)),a<0))",
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arccos(sqrt(-a)/x),or(not(number(a)),a<0))",
#162
"f(x/sqrt(x^2+a),sqrt(x^2+a))",
#163
Expand Down Expand Up @@ -179,7 +179,7 @@ itab = [
#174
"f(1/x^3*1/sqrt(x^2+a),-1/2*sqrt(x^2+a)/a/x^2+1/2*log((sqrt(a)+sqrt(x^2+a))/x)/a^(3/2),or(not(number(a)),a>0))",
#175
"f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arcsec(x/(a^(1/2))),or(not(number(a)),a>0))",
"f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arccos((a^(1/2))/x),or(not(number(a)),a>0))",
#176+
"f(x^2*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/6*x*sqrt((x^2+a^(1/3))^5)-1/24*a^(1/3)*x*sqrt((x^2+a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2+a^(1/3))-1/16*a*log(x+sqrt(x^2+a^(1/3))),or(not(number(a)),a>0))",
#176-
Expand Down Expand Up @@ -818,13 +818,13 @@ hashed_itab = {
"f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*arcsin(x*sqrt(-a/b))/2/sqrt(-a),and(number(a),a<0))"
],
"0.729886": [
"f(1/x*1/sqrt(x^2+a),arcsec(x/sqrt(-a))/sqrt(-a),or(not(number(a)),a<0))",
"f(1/x*1/sqrt(x^2+a),arccos(sqrt(-a)/x)/sqrt(-a),or(not(number(a)),a<0))",
"f(1/x*1/sqrt(x^2+a),-1/sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))",
"f(1/x*1/sqrt(a-x^2),-1/sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))"
],
"1.501230": [
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))",
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arcsec(x/sqrt(-a)),or(not(number(a)),a<0))",
"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arccos(sqrt(-a)/x),or(not(number(a)),a<0))",
"f(sqrt(a-x^2)/x,sqrt(a-x^2)-sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))"
],
"0.666120": [
Expand Down Expand Up @@ -866,7 +866,7 @@ hashed_itab = {
"0.652928": [
"f(x^3/sqrt(x^2+a),1/3*sqrt((x^2+a)^3)-a*sqrt(x^2+a))",
"f(1/x^3*1/sqrt(x^2+a),-1/2*sqrt(x^2+a)/a/x^2+1/2*log((sqrt(a)+sqrt(x^2+a))/x)/a^(3/2),or(not(number(a)),a>0))",
"f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arcsec(x/(a^(1/2))),or(not(number(a)),a>0))"
"f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arccos((a^(1/2))/x),or(not(number(a)),a>0))"
],
"0.764022": [
"f(1/x^2*1/sqrt(x^2+a),-sqrt(x^2+a)/a/x)",
Expand Down
6 changes: 3 additions & 3 deletions tests/integral.coffee
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -251,7 +251,7 @@ test_integral = ->
"0",

#158
"integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",
"integral(1/X*1/sqrt(X^2-2),X)-arccos(sqrt(2)/X)/sqrt(2)",
"0",

#159
Expand All @@ -263,7 +263,7 @@ test_integral = ->
"0",

#161
"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",
"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arccos(sqrt(2)/X)",
"0",

#162
Expand Down Expand Up @@ -322,7 +322,7 @@ test_integral = ->
"0",

#175
"integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2)))",
"integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arccos((2^(1/2))/X)",
"0",

#176+
Expand Down