Mathematical Assistant on Web (integral)

MAW Maxima session: initial call - pass function through Maxima Time 0.467127799988 Maxima 5.13.0 http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) block(load(functs), load(linearalgebra), maw_var : x, maw_var_ori : x, load(/var/www/maw/integral/matchint_short.mac), pfeformat : true) (%i2) (x^2+x+1)/(x^3+x) (%o2) (x^2+x+1)/(x^3+x) (%i3) tex(%,false) (%o3) \$\{\{x\^2\+x\+1\}\\over\{x\^3\+x\}\}\$\$\ MAW Maxima session: Results of suggested substitutions Time 0.883335113525 Maxima 5.13.0 http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) block(load(functs), load(linearalgebra), maw_var : x, maw_var_ori : x, load(/var/www/maw/integral/matchint_short.mac), pfeformat : true, 2 x + x + 1 print(elapsed_run_time()), if not atom(----------) 3 x + x 2 2 x + x + 1 x + x + 1 then (if length(args(----------)) > 1 then print(#, op(----------), #) 3 3 x + x x + x 2 2 x + x + 1 x + x + 1 else (if op(----------) = op(- maw_b) and not atom(args(----------) ) 3 3 1 x + x x + x 2 x + x + 1 then print(#, op(args(----------) ), #))), print(elapsed_run_time())) 3 1 x + x 0.17 # // # 0.17 (%i2) (assume_pos:true,load("/var/www/maw/common/changevar2.mac"), try_substitutions(expr):=trigexpand( rootscontract((savelogarc:logarc,logarc:false, A :diff( changevar2( 'integrate((x^2+x+1)/(x^3+x),x), expr,t,x),t),logarc:savelogarc, A))),tem:map(try_substitutions,[]), maw_print_one_try(tex(tem,false),substresults)) TeX substresults $$\mbox{{}$$\left[ \right] $$ {}}$$ XeT (%o2) "XeT" (%i3) (print(elapsed_run_time()),tex(%,false)) 0.18 (%o3) \$\\mbox\{\{\}XeT\{\}\}\$\$\ MAW Maxima session: looking which algebraic modification changes the function Time 0.78151011467 Maxima 5.13.0 http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) block(load(functs), load(linearalgebra), maw_var : x, maw_var_ori : x, load(/var/www/maw/integral/matchint_short.mac), pfeformat : true, 2 x + x + 1 print(elapsed_run_time()), if not atom(----------) 3 x + x 2 2 x + x + 1 x + x + 1 then (if length(args(----------)) > 1 then print(#, op(----------), #) 3 3 x + x x + x 2 2 x + x + 1 x + x + 1 else (if op(----------) = op(- maw_b) and not atom(args(----------) ) 3 3 1 x + x x + x 2 x + x + 1 then print(#, op(args(----------) ), #))), print(elapsed_run_time())) 3 1 x + x 0.15 # // # 0.15 (%i2) (outf:[],add(f):=(print(f),outf:append(outf,[f])), if expand((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(expand), if factor((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(factor), if fullratsimp((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(fullratsimp), if ratsimp((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(ratsimp), if xthru((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(xthru), if radcan((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(radcan), if logarc((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(logarc_), if rootscontract((x^2+x+1)/(x^3+x)) # (x^2+x+1)/(x^3+x) then add(rootscontract),errcatch(try_functions((x^2+x+1)/(x^3+x))), outf) expand factor TeX sq1 $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX spl $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX sq2 $${{x^2+x+1}\over{\sqrt{x^6+2\,x^4+x^2}}}$$ XeT TeX expand $${{x^2}\over{x^3+x}}+{{x}\over{x^3+x}}+{{1}\over{x^3+x}}$$ XeT TeX factor $${{x^2+x+1}\over{x\,\left(x^2+1\right)}}$$ XeT TeX fullratsimp $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX mapfullratsimp $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX xthru $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX mapxthru $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX radcan $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX logarc_ $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX rootscontract $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX logcontract $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX trigsimp $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX trigreduce $${{1}\over{x^3+x}}+{{x}\over{x^2+1}}+{{1}\over{x^2+1}}$$ XeT TeX trigexp $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX sin2cos $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX cos2sin $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX seccsc $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX divide $${{x^2+x+1}\over{x^3+x}}$$ XeT TeX partfrac $${{1}\over{x^2+1}}+{{1}\over{x}}$$ XeT (%o2) [expand,factor] (%i3) (print(elapsed_run_time()),tex(%,false)) 0.19 (%o3) \$\\left\[\ \{\\it\ expand\}\ \,\ \{\\it\ factor\}\ \\right\]\ \$\$\ MAW Maxima session: === looking for hints === Time 1.24036002159 Maxima 5.13.0 http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) (load(functs), load(linearalgebra), maw_var : x, maw_var_ori : x) (%o1) x (%i2) load(/var/www/maw/integral/matchint.mac) FOUND: root of maw_p exponent abs(h) (%o2) ?\/var\/www\/maw\/integral\/matchint\.mac (%i3) simp:false (%o3) false (%i4) logabs:false (%o4) false (%i5) test_fprime_over_f((x^2+x+1)/(x^3+x)) (%o5) false (%i6) simp:true (%o6) true (%i7) testpart(factor((x^2+x+1)/(x^3+x))) (%o7) false (%i8) testrlf((x^2+x+1)/(x^3+x)) #### testrlf (%o8) true (%i9) testrlfimproper((x^2+x+1)/(x^3+x)) (%o9) false (%i10) testmultiple((x^2+x+1)/(x^3+x)) #### constmul 1 #### constmul 1 (%o10) 1 (%i11) testformula((x^2+x+1)/(x^3+x)) (%o11) false (%i12) test_expand_into_formulas((x^2+x+1)/(x^3+x)) silent testformula 7 (%o12) false (%i13) testsubst((x^2+x+1)/(x^3+x)) ***** looking for sine a cosine ***** looking for log and atan ***** looking for root exponent 1 set of bases: {} ***** looking for root with rootscontract exponent 1 set of bases: {} ***** looking for R(sin(x),cos(x)) ***** looking for powers FOUND: power of x (exponent 2 ) in function (x^2+x+1)/(x^3+x) MAW comment: Trying x^2 = new_maw_var in integral of (x^2+x+1)/(x^3+x) changevar2: using plain changevar result after substitution: -(-new_maw_var+sqrt(new_maw_var)-1)/(2*new_maw_var^2+2*new_maw_var) false FOUND: power of x^3+x (exponent -1 ) in function (x^2+x+1)/(x^3+x) MAW comment: Trying x^3+x = new_maw_var in integral of (x^2+x+1)/(x^3+x) changevar2: using plain changevar result after substitution: (((19683*2^(1/3)*%i-6561*2^(1/3)*sqrt(3))*new_maw_var^5 +sqrt(27*new_maw_var^2+4)*((2187*2^(1/3)*sqrt(3)*%i-2187*2^(1/3)) *new_maw_var^4 +(486*2^(1/3)*sqrt(3)*%i-486*2^(1/3))*new_maw_var^3 +(324*2^(1/3)*sqrt(3)*%i-324*2^(1/3))*new_maw_var^2 +(54*2^(1/3)*sqrt(3)*%i-54*2^(1/3))*new_maw_var +6*2^(1/3)*sqrt(3)*%i-6*2^(1/3)) +(4374*2^(1/3)*%i-1458*2^(1/3)*sqrt(3))*new_maw_var^4 +(4374*2^(1/3)*%i-1458*2^(1/3)*sqrt(3))*new_maw_var^3 +(810*2^(1/3)*%i-270*2^(1/3)*sqrt(3))*new_maw_var^2 +(216*2^(1/3)*%i-72*2^(1/3)*sqrt(3))*new_maw_var+24*2^(1/3)*%i -8*2^(1/3)*sqrt(3)) *(sqrt(27*new_maw_var^2+4)+3*sqrt(3)*new_maw_var)^(2/3) +((-13122*2^(2/3)*sqrt(3)*%i-13122*2^(2/3))*new_maw_var^5 +sqrt(27*new_maw_var^2+4)*((-4374*2^(2/3)*%i-1458*2^(2/3)*sqrt(3)) *new_maw_var^4 +(729*2^(2/3)*%i+243*2^(2/3)*sqrt(3)) *new_maw_var^3 +(-648*2^(2/3)*%i-216*2^(2/3)*sqrt(3)) *new_maw_var^2 +(81*2^(2/3)*%i+27*2^(2/3)*sqrt(3))*new_maw_var -12*2^(2/3)*%i-4*2^(2/3)*sqrt(3)) +(2187*2^(2/3)*sqrt(3)*%i+2187*2^(2/3))*new_maw_var^4 +(-2916*2^(2/3)*sqrt(3)*%i-2916*2^(2/3))*new_maw_var^3 +(405*2^(2/3)*sqrt(3)*%i+405*2^(2/3))*new_maw_var^2 +(-144*2^(2/3)*sqrt(3)*%i-144*2^(2/3))*new_maw_var+12*2^(2/3)*sqrt(3)*%i +12*2^(2/3)) *(sqrt(27*new_maw_var^2+4)+3*sqrt(3)*new_maw_var)^(1/3) +78732*sqrt(3)*new_maw_var^6 +sqrt(27*new_maw_var^2+4)*(26244*new_maw_var^5+5832*new_maw_var^3 +288*new_maw_var) +23328*sqrt(3)*new_maw_var^4+1944*sqrt(3)*new_maw_var^2+32*sqrt(3)) /(236196*sqrt(3)*new_maw_var^7+sqrt(27*new_maw_var^2+4) *(78732*new_maw_var^6+17496*new_maw_var^4 +864*new_maw_var^2) +69984*sqrt(3)*new_maw_var^5 +5832*sqrt(3)*new_maw_var^3 +96*sqrt(3)*new_maw_var) MAW comment: Trying 1/(x^3+x) = new_maw_var in integral of (x^2+x+1)/(x^3+x) changevar2: using plain changevar result after substitution: -(32*sqrt(3)*new_maw_var^6+(sqrt(4*new_maw_var^2+27)+3*sqrt(3))^(1/3) *(new_maw_var^(2/3) *((12*2^(2/3)*sqrt(3)*%i+12*2^(2/3))*new_maw_var^5 +(-144*2^(2/3)*sqrt(3)*%i-144*2^(2/3)) *new_maw_var^4 +(405*2^(2/3)*sqrt(3)*%i+405*2^(2/3)) *new_maw_var^3 +(-2916*2^(2/3)*sqrt(3)*%i-2916*2^(2/3)) *new_maw_var^2 +(2187*2^(2/3)*sqrt(3)*%i+2187*2^(2/3)) *new_maw_var-13122*2^(2/3)*sqrt(3)*%i -13122*2^(2/3)) +new_maw_var^(2/3)*sqrt(4*new_maw_var^2+27) *((-12*2^(2/3)*%i -4*2^(2/3)*sqrt(3)) *new_maw_var^4 +(81*2^(2/3)*%i +27*2^(2/3)*sqrt(3)) *new_maw_var^3 +(-648*2^(2/3)*%i -216*2^(2/3)*sqrt(3)) *new_maw_var^2 +(729*2^(2/3)*%i +243*2^(2/3)*sqrt(3)) *new_maw_var-4374*2^(2/3)*%i -1458*2^(2/3)*sqrt(3))) +(sqrt(4*new_maw_var^2+27)+3*sqrt(3))^(2/3) *(new_maw_var^(1/3) *((24*2^(1/3)*%i-8*2^(1/3)*sqrt(3))*new_maw_var^5 +(216*2^(1/3)*%i-72*2^(1/3)*sqrt(3)) *new_maw_var^4 +(810*2^(1/3)*%i-270*2^(1/3)*sqrt(3)) *new_maw_var^3 +(4374*2^(1/3)*%i-1458*2^(1/3)*sqrt(3)) *new_maw_var^2 +(4374*2^(1/3)*%i-1458*2^(1/3)*sqrt(3)) *new_maw_var+19683*2^(1/3)*%i -6561*2^(1/3)*sqrt(3)) +new_maw_var^(1/3)*sqrt(4*new_maw_var^2+27) *((6*2^(1/3)*sqrt(3)*%i -6*2^(1/3)) *new_maw_var^4 +(54*2^(1/3)*sqrt(3)*%i -54*2^(1/3)) *new_maw_var^3 +(324*2^(1/3)*sqrt(3)*%i -324*2^(1/3)) *new_maw_var^2 +(486*2^(1/3)*sqrt(3)*%i -486*2^(1/3)) *new_maw_var +2187*2^(1/3)*sqrt(3)*%i -2187*2^(1/3))) +sqrt(4*new_maw_var^2+27) *(288*new_maw_var^4+5832*new_maw_var^2+26244) +1944*sqrt(3)*new_maw_var^4 +23328*sqrt(3)*new_maw_var^2+78732*sqrt(3)) /(96*sqrt(3)*new_maw_var^7+sqrt(4*new_maw_var^2+27) *(864*new_maw_var^5+17496*new_maw_var^3 +78732*new_maw_var) +5832*sqrt(3)*new_maw_var^5 +69984*sqrt(3)*new_maw_var^3 +236196*sqrt(3)*new_maw_var) FOUND: power of x (exponent 3 ) in function (x^2+x+1)/(x^3+x) MAW comment: Trying x^3 = new_maw_var in integral of (x^2+x+1)/(x^3+x) changevar2: using plain changevar result after substitution: (2*new_maw_var^(2/3)+(-sqrt(3)*%i-1)*new_maw_var^(1/3)+sqrt(3)*%i-1) /(6*new_maw_var^(5/3)+(3*sqrt(3)*%i-3)*new_maw_var) false [] (%o13) false (%i14) test_ostrogradski_method(rootscontract((x^2+x+1)/(x^3+x))) (%o14) false (%i15) testrlfxthru((x^2+x+1)/(x^3+x)) (%o15) false (%i16) load(ntrig) (%o16) ?\/usr\/share\/maxima\/5\.13\.0\/share\/trigonometry\/ntrig\.mac (%i17) testpartfrac((x^2+x+1)/(x^3+x)) #### testpartfrac (%o17) "testpartfrac"

Integrální počet s asistencí

Maxima sessions (click to unfold)

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