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

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

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4 changes: 2 additions & 2 deletions .gitattributes
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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
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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
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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