/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/

/* [wxMaxima: input   start ] */
example(sinc);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
example(commutative);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^2));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^2),x);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^1),x);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^3),x);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
-log(x^2-x+1)/6+atan((2*x-1)/sqrt(3))/sqrt(3)+log(x+1)/3;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
taylor(%, x, 0, 8);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
((log((sqrt(3)*%i+3)/3)-log(-(sqrt(3)*%i-3)/3))*%i)/(2*sqrt(3));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ratsimp(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
radcan(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
factor(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
expand(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
trigsimp(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
trigreduce(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
wxplot2d([%], [x,-5,5])$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
float((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6), numer;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
trigreduce(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor()(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor()(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor()(sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6)));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
gfactor(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
radcan(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
polarform(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform((sqrt(3)*%i*log(sqrt(3)*%i+4)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
taylor((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6, x, 0, 8);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
if numer#false then numer:false else numer:true;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
taylor(-log(x^2-x+1)/6+atan((2*x-1)/sqrt(3))/sqrt(3)+log(x+1)/3, x, 0, 16);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
taylor(-log(x^2-x+1)/6+atan((2*x-1)/sqrt(3))/sqrt(3)+log(x+1)/3, x, 0, 30);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
taylor(-log(x^2-x+1)/6+atan((2*x-1)/sqrt(3))/sqrt(3)+log(x+1)/3, x, 0, 100);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform(taylor(-log(x^2-x+1)/6+atan((2*x-1)/sqrt(3))/sqrt(3)+log(x+1)/3, x, 0, 100));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform(((log((sqrt(3)*%i+3)/3)-log(-(sqrt(3)*%i-3)/3))*%i)/(2*sqrt(3)));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rectform((sqrt(3)*%i*log(sqrt(3)*%i+3)-sqrt(3)*%i*log(3-sqrt(3)*%i))/6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^3),x)-(-x^100/100+x^97/97-x^94/94+x^91/91-x^88/88+x^85/85-x^82/82
 +x^79/79-x^76/76+x^73/73-x^70/70+x^67/67-x^64/64+x^61/61-x^58/58+x^55/55-x^52/52+x^49/49
 -x^46/46+x^43/43-x^40/40+x^37/37-x^34/34+x^31/31-x^28/28+x^25/25-x^22/22+x^19/19-x^16/16
 +x^13/13-x^10/10+x^7/7-x^4/4+x-%pi/(6*sqrt(3)));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot(%,[x,0,10]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(%,[x,0,10]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^3),x)-(-x^100/100+x^97/97-x^94/94+x^91/91-x^88/88+x^85/85-x^82/82
 +x^79/79-x^76/76+x^73/73-x^70/70+x^67/67-x^64/64+x^61/61-x^58/58+x^55/55-x^52/52+x^49/49
 -x^46/46+x^43/43-x^40/40+x^37/37-x^34/34+x^31/31-x^28/28+x^25/25-x^22/22+x^19/19-x^16/16
 +x^13/13-x^10/10+x^7/7-x^4/4+x-%pi/(6*sqrt(3)));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(%,[x,0,10]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
integrate(1/(1+x^3),x)-(-x^100/100+x^97/97-x^94/94+x^91/91-x^88/88+x^85/85-x^82/82
 +x^79/79-x^76/76+x^73/73-x^70/70+x^67/67-x^64/64+x^61/61-x^58/58+x^55/55-x^52/52+x^49/49
 -x^46/46+x^43/43-x^40/40+x^37/37-x^34/34+x^31/31-x^28/28+x^25/25-x^22/22+x^19/19-x^16/16
 +x^13/13-x^10/10+x^7/7-x^4/4+x-%pi/(6*sqrt(3)));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(%,[x,0,1]);
plot2d(integrate(1/(1+x^3),x)-(-x^100/100+x^97/97-x^94/94+x^91/91-x^88/88+x^85/85
 -x^82/82+x^79/79-x^76/76+x^73/73-x^70/70+x^67/67-x^64/64+x^61/61-x^58/58+x^55/55-x^52/52
 +x^49/49-x^46/46+x^43/43-x^40/40+x^37/37-x^34/34+x^31/31-x^28/28+x^25/25-x^22/22+x^19/19
 -x^16/16+x^13/13-x^10/10+x^7/7-x^4/4+x-%pi/(6*sqrt(3))),[x,0,0.8]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
fpprec : 32;
plot2d(integrate(1/(1+x^3),x)-(-x^100/100+x^97/97-x^94/94+x^91/91-x^88/88+x^85/85
 -x^82/82+x^79/79-x^76/76+x^73/73-x^70/70+x^67/67-x^64/64+x^61/61-x^58/58+x^55/55-x^52/52
 +x^49/49-x^46/46+x^43/43-x^40/40+x^37/37-x^34/34+x^31/31-x^28/28+x^25/25-x^22/22+x^19/19
 -x^16/16+x^13/13-x^10/10+x^7/7-x^4/4+x-%pi/(6*sqrt(3))),[x,0,0.1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(integrate(1/(1+x^3),x),[x,0,0.1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(integrate(1/(1+x^3),x),[x,0,10]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(integrate(1/(1+x^3),x),[x,/1,20]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(integrate(1/(1+x^3),x),[x,-1,20]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(integrate(1/(1+x^3),x),[x,-10,20]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
log10(x) := log(x) / log(10);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
f(x):=integrate(1/(1+x^3),x);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=x^100/100-x^97/97+x^94/94-x^91/91+x^88/88-x^85/85+x^82/82-x^79/79+x^76/76
 -;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=x^100/100-x^97/97+x^94/94-x^91/91+x^88/88-x^85/85+x^82/82-x^79/79+x^76/76
 -
x^73/73+x^70/70-x^67/67+x^64/64-x^61/61+x^58/58-x^55/55+x^52/52-x^49/49+x^46/46-x^43/43
 +x^40/40-x^37/37+x^34/34-x^31/31+x^28/28-x^25/25+x^22/22-x^19/19+
x^16/16-x^13/13+x^10/10-x^7/7+x^4/4-x+%pi/(6*sqrt(3))$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=x^100/100-x^97/97+x^94/94-x^91/91+x^88/88-x^85/85+x^82/82-x^79/79+x^76/76
 -
x^73/73+x^70/70-x^67/67+x^64/64-x^61/61+x^58/58-x^55/55+x^52/52-x^49/49+x^46/46-x^43/43
 +x^40/40-x^37/37+x^34/34-x^31/31+x^28/28-x^25/25+x^22/22-x^19/19+
x^16/16-x^13/13+x^10/10-x^7/7+x^4/4-x+%pi/(6*sqrt(3))$
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(0);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
fpprec : 32;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(log10(abs(f(x)-ft100(x))),[x,-1,10]);
plot2d(log10(abs(f(x)-ft100(x))),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(log10(abs(f(x)-ft100(x))),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
bfloat(%);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
fpprec : 32;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x)-ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=x^100/100-x^97/97+x^94/94-x^91/91+x^88/88-x^85/85+x^82/82-x^79/79+x^76/76
 -
x^73/73+x^70/70-x^67/67+x^64/64-x^61/61+x^58/58-x^55/55+x^52/52-x^49/49+x^46/46-x^43/43
 +x^40/40-x^37/37+x^34/34-x^31/31+x^28/28-x^25/25+x^22/22-x^19/19+
x^16/16-x^13/13+x^10/10-x^7/7+x^4/4-x-(3^(-1/2)*%pi)/(3*2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x)-ft100(x),[x,-1,1]);
plot2d(f(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=((log((sqrt(3)*%i+3)/3)-log(-(sqrt(3)*%i-3)/3))*%i)/(2*sqrt(3))+x-x^4/4
 +x^7/7-x^10/10+x^13/13-x^16/16+x^19/19-x^22/22+x^25/25-x^28/28+x^31/31-
x^34/34+x^37/37-x^40/40+x^43/43-x^46/46+x^49/49-x^52/52+x^55/55-x^58/58+x^61/61-x^64/64
 +x^67/67-x^70/70+x^73/73-x^76/76+x^79/79-x^82/82+x^85/85-x^88/88+
x^91/91-x^94/94+x^97/97-x^100/100+(3^(-1/2)*%pi)/(3*2)$
plot2d(f(x)-ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x)-ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
ft100(x):=x-x^4/4+x^7/7-x^10/10+x^13/13-x^16/16+x^19/19-x^22/22+x^25/25-x^28/28+x^31/31
 -x^34/34+x^37/37-x^40/40+x^43/43-x^46/46+x^49/49-x^52/52+x^55/55-x^58/58+x^61/61-x^64/64
 +x^67/67-x^70/70+x^73/73-x^76/76+x^79/79-x^82/82+x^85/85-x^88/88+x^91/91-x^94/94+x^97/97
 -x^100/100-(3^(-1/2)*%pi)/(3*2);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x)-ft100(x),[x,-1,1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(f(x)-ft100(x),[x,-0.9,.9]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
plot2d(log10(abs(f(x)-ft100(x))),[x,-0.9,.9]);
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$