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3.40.15 \(\int \frac {-32-32 x-3136 x^2-5856 x^3-135264 x^4-361536 x^5-3470656 x^6-11342464 x^7-60505088 x^8-209432832 x^9-761634048 x^{10}-2431822848 x^{11}-6896916992 x^{12}-18247276544 x^{13}-42386477056 x^{14}-87747545088 x^{15}-160647395328 x^{16}-251744145408 x^{17}-329327366144 x^{18}-354061008896 x^{19}-305923072000 x^{20}-201710469120 x^{21}-86671294464 x^{22}-4145971200 x^{23}+30720819200 x^{24}+31082479616 x^{25}+18860670976 x^{26}+8172208128 x^{27}+2618032128 x^{28}+614203392 x^{29}+100925440 x^{30}+10485760 x^{31}+524288 x^{32}}{131072 x^{17}+1114112 x^{18}+4456448 x^{19}+11141120 x^{20}+19496960 x^{21}+25346048 x^{22}+25346048 x^{23}+19914752 x^{24}+12446720 x^{25}+6223360 x^{26}+2489344 x^{27}+792064 x^{28}+198016 x^{29}+38080 x^{30}+5440 x^{31}+544 x^{32}+34 x^{33}+x^{34}} \, dx\)

Optimal. Leaf size=21 \[ 1+\left (3+\frac {\left (\frac {1}{x}+x\right )^2}{(2+x)^2}\right )^8+\log (2) \]

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Rubi [B]  time = 13.79, antiderivative size = 257, normalized size of antiderivative = 12.24, number of steps used = 2, number of rules used = 1, integrand size = 252, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {2074} \begin {gather*} \frac {1}{65536 x^{16}}-\frac {1}{8192 x^{15}}+\frac {73}{32768 x^{14}}-\frac {451}{32768 x^{13}}+\frac {35209}{262144 x^{12}}-\frac {86793}{131072 x^{11}}+\frac {2331487}{524288 x^{10}}-\frac {9314723}{524288 x^9}+\frac {751825061}{8388608 x^8}-\frac {610621687}{2097152 x^7}+\frac {9584001347}{8388608 x^6}-\frac {25159927717}{8388608 x^5}+\frac {618957835629}{67108864 x^4}-\frac {647127286119}{33554432 x^3}+\frac {6154395725533}{134217728 x^2}-\frac {60269601838595}{134217728 (x+2)}+\frac {365887609840925}{134217728 (x+2)^2}-\frac {303271381877625}{33554432 (x+2)^3}+\frac {1712660764398125}{67108864 (x+2)^4}-\frac {471710683246875}{8388608 (x+2)^5}+\frac {886272205671875}{8388608 (x+2)^6}-\frac {346786757265625}{2097152 (x+2)^7}+\frac {1871087401953125}{8388608 (x+2)^8}-\frac {133520798828125}{524288 (x+2)^9}+\frac {131157099609375}{524288 (x+2)^{10}}-\frac {27015771484375}{131072 (x+2)^{11}}+\frac {37592041015625}{262144 (x+2)^{12}}-\frac {2628173828125}{32768 (x+2)^{13}}+\frac {1177978515625}{32768 (x+2)^{14}}-\frac {91552734375}{8192 (x+2)^{15}}+\frac {152587890625}{65536 (x+2)^{16}}-\frac {10099142339069}{134217728 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-32 - 32*x - 3136*x^2 - 5856*x^3 - 135264*x^4 - 361536*x^5 - 3470656*x^6 - 11342464*x^7 - 60505088*x^8 -
209432832*x^9 - 761634048*x^10 - 2431822848*x^11 - 6896916992*x^12 - 18247276544*x^13 - 42386477056*x^14 - 877
47545088*x^15 - 160647395328*x^16 - 251744145408*x^17 - 329327366144*x^18 - 354061008896*x^19 - 305923072000*x
^20 - 201710469120*x^21 - 86671294464*x^22 - 4145971200*x^23 + 30720819200*x^24 + 31082479616*x^25 + 188606709
76*x^26 + 8172208128*x^27 + 2618032128*x^28 + 614203392*x^29 + 100925440*x^30 + 10485760*x^31 + 524288*x^32)/(
131072*x^17 + 1114112*x^18 + 4456448*x^19 + 11141120*x^20 + 19496960*x^21 + 25346048*x^22 + 25346048*x^23 + 19
914752*x^24 + 12446720*x^25 + 6223360*x^26 + 2489344*x^27 + 792064*x^28 + 198016*x^29 + 38080*x^30 + 5440*x^31
 + 544*x^32 + 34*x^33 + x^34),x]

[Out]

1/(65536*x^16) - 1/(8192*x^15) + 73/(32768*x^14) - 451/(32768*x^13) + 35209/(262144*x^12) - 86793/(131072*x^11
) + 2331487/(524288*x^10) - 9314723/(524288*x^9) + 751825061/(8388608*x^8) - 610621687/(2097152*x^7) + 9584001
347/(8388608*x^6) - 25159927717/(8388608*x^5) + 618957835629/(67108864*x^4) - 647127286119/(33554432*x^3) + 61
54395725533/(134217728*x^2) - 10099142339069/(134217728*x) + 152587890625/(65536*(2 + x)^16) - 91552734375/(81
92*(2 + x)^15) + 1177978515625/(32768*(2 + x)^14) - 2628173828125/(32768*(2 + x)^13) + 37592041015625/(262144*
(2 + x)^12) - 27015771484375/(131072*(2 + x)^11) + 131157099609375/(524288*(2 + x)^10) - 133520798828125/(5242
88*(2 + x)^9) + 1871087401953125/(8388608*(2 + x)^8) - 346786757265625/(2097152*(2 + x)^7) + 886272205671875/(
8388608*(2 + x)^6) - 471710683246875/(8388608*(2 + x)^5) + 1712660764398125/(67108864*(2 + x)^4) - 30327138187
7625/(33554432*(2 + x)^3) + 365887609840925/(134217728*(2 + x)^2) - 60269601838595/(134217728*(2 + x))

Rule 2074

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{4096 x^{17}}+\frac {15}{8192 x^{16}}-\frac {511}{16384 x^{15}}+\frac {5863}{32768 x^{14}}-\frac {105627}{65536 x^{13}}+\frac {954723}{131072 x^{12}}-\frac {11657435}{262144 x^{11}}+\frac {83832507}{524288 x^{10}}-\frac {751825061}{1048576 x^9}+\frac {4274351809}{2097152 x^8}-\frac {28752004041}{4194304 x^7}+\frac {125799638585}{8388608 x^6}-\frac {618957835629}{16777216 x^5}+\frac {1941381858357}{33554432 x^4}-\frac {6154395725533}{67108864 x^3}+\frac {10099142339069}{134217728 x^2}-\frac {152587890625}{4096 (2+x)^{17}}+\frac {1373291015625}{8192 (2+x)^{16}}-\frac {8245849609375}{16384 (2+x)^{15}}+\frac {34166259765625}{32768 (2+x)^{14}}-\frac {112776123046875}{65536 (2+x)^{13}}+\frac {297173486328125}{131072 (2+x)^{12}}-\frac {655785498046875}{262144 (2+x)^{11}}+\frac {1201687189453125}{524288 (2+x)^{10}}-\frac {1871087401953125}{1048576 (2+x)^9}+\frac {2427507300859375}{2097152 (2+x)^8}-\frac {2658816617015625}{4194304 (2+x)^7}+\frac {2358553416234375}{8388608 (2+x)^6}-\frac {1712660764398125}{16777216 (2+x)^5}+\frac {909814145632875}{33554432 (2+x)^4}-\frac {365887609840925}{67108864 (2+x)^3}+\frac {60269601838595}{134217728 (2+x)^2}\right ) \, dx\\ &=\frac {1}{65536 x^{16}}-\frac {1}{8192 x^{15}}+\frac {73}{32768 x^{14}}-\frac {451}{32768 x^{13}}+\frac {35209}{262144 x^{12}}-\frac {86793}{131072 x^{11}}+\frac {2331487}{524288 x^{10}}-\frac {9314723}{524288 x^9}+\frac {751825061}{8388608 x^8}-\frac {610621687}{2097152 x^7}+\frac {9584001347}{8388608 x^6}-\frac {25159927717}{8388608 x^5}+\frac {618957835629}{67108864 x^4}-\frac {647127286119}{33554432 x^3}+\frac {6154395725533}{134217728 x^2}-\frac {10099142339069}{134217728 x}+\frac {152587890625}{65536 (2+x)^{16}}-\frac {91552734375}{8192 (2+x)^{15}}+\frac {1177978515625}{32768 (2+x)^{14}}-\frac {2628173828125}{32768 (2+x)^{13}}+\frac {37592041015625}{262144 (2+x)^{12}}-\frac {27015771484375}{131072 (2+x)^{11}}+\frac {131157099609375}{524288 (2+x)^{10}}-\frac {133520798828125}{524288 (2+x)^9}+\frac {1871087401953125}{8388608 (2+x)^8}-\frac {346786757265625}{2097152 (2+x)^7}+\frac {886272205671875}{8388608 (2+x)^6}-\frac {471710683246875}{8388608 (2+x)^5}+\frac {1712660764398125}{67108864 (2+x)^4}-\frac {303271381877625}{33554432 (2+x)^3}+\frac {365887609840925}{134217728 (2+x)^2}-\frac {60269601838595}{134217728 (2+x)}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.05, size = 161, normalized size = 7.67 \begin {gather*} \frac {1+112 x^2+96 x^3+5520 x^4+9408 x^5+160832 x^6+397824 x^7+3159968 x^8+9542400 x^9+45179904 x^{10}+143786496 x^{11}+484675072 x^{12}+1425629184 x^{13}+3824880640 x^{14}+9449846784 x^{15}+16583389952 x^{16}+6795046912 x^{17}-56850415616 x^{18}-191661137920 x^{19}-349689733120 x^{20}-439798726656 x^{21}-410371440640 x^{22}-293418598400 x^{23}-163127910400 x^{24}-70774489088 x^{25}-23828037632 x^{26}-6127091712 x^{27}-1167392768 x^{28}-155975680 x^{29}-13107200 x^{30}-524288 x^{31}}{x^{16} (2+x)^{16}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-32 - 32*x - 3136*x^2 - 5856*x^3 - 135264*x^4 - 361536*x^5 - 3470656*x^6 - 11342464*x^7 - 60505088*
x^8 - 209432832*x^9 - 761634048*x^10 - 2431822848*x^11 - 6896916992*x^12 - 18247276544*x^13 - 42386477056*x^14
 - 87747545088*x^15 - 160647395328*x^16 - 251744145408*x^17 - 329327366144*x^18 - 354061008896*x^19 - 30592307
2000*x^20 - 201710469120*x^21 - 86671294464*x^22 - 4145971200*x^23 + 30720819200*x^24 + 31082479616*x^25 + 188
60670976*x^26 + 8172208128*x^27 + 2618032128*x^28 + 614203392*x^29 + 100925440*x^30 + 10485760*x^31 + 524288*x
^32)/(131072*x^17 + 1114112*x^18 + 4456448*x^19 + 11141120*x^20 + 19496960*x^21 + 25346048*x^22 + 25346048*x^2
3 + 19914752*x^24 + 12446720*x^25 + 6223360*x^26 + 2489344*x^27 + 792064*x^28 + 198016*x^29 + 38080*x^30 + 544
0*x^31 + 544*x^32 + 34*x^33 + x^34),x]

[Out]

(1 + 112*x^2 + 96*x^3 + 5520*x^4 + 9408*x^5 + 160832*x^6 + 397824*x^7 + 3159968*x^8 + 9542400*x^9 + 45179904*x
^10 + 143786496*x^11 + 484675072*x^12 + 1425629184*x^13 + 3824880640*x^14 + 9449846784*x^15 + 16583389952*x^16
 + 6795046912*x^17 - 56850415616*x^18 - 191661137920*x^19 - 349689733120*x^20 - 439798726656*x^21 - 4103714406
40*x^22 - 293418598400*x^23 - 163127910400*x^24 - 70774489088*x^25 - 23828037632*x^26 - 6127091712*x^27 - 1167
392768*x^28 - 155975680*x^29 - 13107200*x^30 - 524288*x^31)/(x^16*(2 + x)^16)

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fricas [B]  time = 0.73, size = 240, normalized size = 11.43 \begin {gather*} -\frac {524288 \, x^{31} + 13107200 \, x^{30} + 155975680 \, x^{29} + 1167392768 \, x^{28} + 6127091712 \, x^{27} + 23828037632 \, x^{26} + 70774489088 \, x^{25} + 163127910400 \, x^{24} + 293418598400 \, x^{23} + 410371440640 \, x^{22} + 439798726656 \, x^{21} + 349689733120 \, x^{20} + 191661137920 \, x^{19} + 56850415616 \, x^{18} - 6795046912 \, x^{17} - 16583389952 \, x^{16} - 9449846784 \, x^{15} - 3824880640 \, x^{14} - 1425629184 \, x^{13} - 484675072 \, x^{12} - 143786496 \, x^{11} - 45179904 \, x^{10} - 9542400 \, x^{9} - 3159968 \, x^{8} - 397824 \, x^{7} - 160832 \, x^{6} - 9408 \, x^{5} - 5520 \, x^{4} - 96 \, x^{3} - 112 \, x^{2} - 1}{x^{32} + 32 \, x^{31} + 480 \, x^{30} + 4480 \, x^{29} + 29120 \, x^{28} + 139776 \, x^{27} + 512512 \, x^{26} + 1464320 \, x^{25} + 3294720 \, x^{24} + 5857280 \, x^{23} + 8200192 \, x^{22} + 8945664 \, x^{21} + 7454720 \, x^{20} + 4587520 \, x^{19} + 1966080 \, x^{18} + 524288 \, x^{17} + 65536 \, x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((524288*x^32+10485760*x^31+100925440*x^30+614203392*x^29+2618032128*x^28+8172208128*x^27+18860670976
*x^26+31082479616*x^25+30720819200*x^24-4145971200*x^23-86671294464*x^22-201710469120*x^21-305923072000*x^20-3
54061008896*x^19-329327366144*x^18-251744145408*x^17-160647395328*x^16-87747545088*x^15-42386477056*x^14-18247
276544*x^13-6896916992*x^12-2431822848*x^11-761634048*x^10-209432832*x^9-60505088*x^8-11342464*x^7-3470656*x^6
-361536*x^5-135264*x^4-5856*x^3-3136*x^2-32*x-32)/(x^34+34*x^33+544*x^32+5440*x^31+38080*x^30+198016*x^29+7920
64*x^28+2489344*x^27+6223360*x^26+12446720*x^25+19914752*x^24+25346048*x^23+25346048*x^22+19496960*x^21+111411
20*x^20+4456448*x^19+1114112*x^18+131072*x^17),x, algorithm="fricas")

[Out]

-(524288*x^31 + 13107200*x^30 + 155975680*x^29 + 1167392768*x^28 + 6127091712*x^27 + 23828037632*x^26 + 707744
89088*x^25 + 163127910400*x^24 + 293418598400*x^23 + 410371440640*x^22 + 439798726656*x^21 + 349689733120*x^20
 + 191661137920*x^19 + 56850415616*x^18 - 6795046912*x^17 - 16583389952*x^16 - 9449846784*x^15 - 3824880640*x^
14 - 1425629184*x^13 - 484675072*x^12 - 143786496*x^11 - 45179904*x^10 - 9542400*x^9 - 3159968*x^8 - 397824*x^
7 - 160832*x^6 - 9408*x^5 - 5520*x^4 - 96*x^3 - 112*x^2 - 1)/(x^32 + 32*x^31 + 480*x^30 + 4480*x^29 + 29120*x^
28 + 139776*x^27 + 512512*x^26 + 1464320*x^25 + 3294720*x^24 + 5857280*x^23 + 8200192*x^22 + 8945664*x^21 + 74
54720*x^20 + 4587520*x^19 + 1966080*x^18 + 524288*x^17 + 65536*x^16)

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giac [B]  time = 0.13, size = 163, normalized size = 7.76 \begin {gather*} -\frac {524288 \, x^{31} + 13107200 \, x^{30} + 155975680 \, x^{29} + 1167392768 \, x^{28} + 6127091712 \, x^{27} + 23828037632 \, x^{26} + 70774489088 \, x^{25} + 163127910400 \, x^{24} + 293418598400 \, x^{23} + 410371440640 \, x^{22} + 439798726656 \, x^{21} + 349689733120 \, x^{20} + 191661137920 \, x^{19} + 56850415616 \, x^{18} - 6795046912 \, x^{17} - 16583389952 \, x^{16} - 9449846784 \, x^{15} - 3824880640 \, x^{14} - 1425629184 \, x^{13} - 484675072 \, x^{12} - 143786496 \, x^{11} - 45179904 \, x^{10} - 9542400 \, x^{9} - 3159968 \, x^{8} - 397824 \, x^{7} - 160832 \, x^{6} - 9408 \, x^{5} - 5520 \, x^{4} - 96 \, x^{3} - 112 \, x^{2} - 1}{{\left (x^{2} + 2 \, x\right )}^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((524288*x^32+10485760*x^31+100925440*x^30+614203392*x^29+2618032128*x^28+8172208128*x^27+18860670976
*x^26+31082479616*x^25+30720819200*x^24-4145971200*x^23-86671294464*x^22-201710469120*x^21-305923072000*x^20-3
54061008896*x^19-329327366144*x^18-251744145408*x^17-160647395328*x^16-87747545088*x^15-42386477056*x^14-18247
276544*x^13-6896916992*x^12-2431822848*x^11-761634048*x^10-209432832*x^9-60505088*x^8-11342464*x^7-3470656*x^6
-361536*x^5-135264*x^4-5856*x^3-3136*x^2-32*x-32)/(x^34+34*x^33+544*x^32+5440*x^31+38080*x^30+198016*x^29+7920
64*x^28+2489344*x^27+6223360*x^26+12446720*x^25+19914752*x^24+25346048*x^23+25346048*x^22+19496960*x^21+111411
20*x^20+4456448*x^19+1114112*x^18+131072*x^17),x, algorithm="giac")

[Out]

-(524288*x^31 + 13107200*x^30 + 155975680*x^29 + 1167392768*x^28 + 6127091712*x^27 + 23828037632*x^26 + 707744
89088*x^25 + 163127910400*x^24 + 293418598400*x^23 + 410371440640*x^22 + 439798726656*x^21 + 349689733120*x^20
 + 191661137920*x^19 + 56850415616*x^18 - 6795046912*x^17 - 16583389952*x^16 - 9449846784*x^15 - 3824880640*x^
14 - 1425629184*x^13 - 484675072*x^12 - 143786496*x^11 - 45179904*x^10 - 9542400*x^9 - 3159968*x^8 - 397824*x^
7 - 160832*x^6 - 9408*x^5 - 5520*x^4 - 96*x^3 - 112*x^2 - 1)/(x^2 + 2*x)^16

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maple [B]  time = 0.12, size = 162, normalized size = 7.71

method result size
norman \(\frac {-524288 x^{31}-13107200 x^{30}-155975680 x^{29}-1167392768 x^{28}-6127091712 x^{27}-23828037632 x^{26}-70774489088 x^{25}-163127910400 x^{24}-293418598400 x^{23}-410371440640 x^{22}-439798726656 x^{21}-349689733120 x^{20}-191661137920 x^{19}-56850415616 x^{18}+6795046912 x^{17}+16583389952 x^{16}+9449846784 x^{15}+3824880640 x^{14}+1425629184 x^{13}+484675072 x^{12}+143786496 x^{11}+45179904 x^{10}+9542400 x^{9}+3159968 x^{8}+397824 x^{7}+160832 x^{6}+9408 x^{5}+5520 x^{4}+96 x^{3}+112 x^{2}+1}{x^{16} \left (2+x \right )^{16}}\) \(162\)
default \(\frac {618957835629}{67108864 x^{4}}-\frac {25159927717}{8388608 x^{5}}-\frac {91552734375}{8192 \left (2+x \right )^{15}}+\frac {152587890625}{65536 \left (2+x \right )^{16}}+\frac {1871087401953125}{8388608 \left (2+x \right )^{8}}-\frac {133520798828125}{524288 \left (2+x \right )^{9}}+\frac {131157099609375}{524288 \left (2+x \right )^{10}}-\frac {27015771484375}{131072 \left (2+x \right )^{11}}+\frac {37592041015625}{262144 \left (2+x \right )^{12}}-\frac {2628173828125}{32768 \left (2+x \right )^{13}}+\frac {1177978515625}{32768 \left (2+x \right )^{14}}-\frac {303271381877625}{33554432 \left (2+x \right )^{3}}+\frac {1712660764398125}{67108864 \left (2+x \right )^{4}}-\frac {471710683246875}{8388608 \left (2+x \right )^{5}}+\frac {886272205671875}{8388608 \left (2+x \right )^{6}}-\frac {346786757265625}{2097152 \left (2+x \right )^{7}}-\frac {60269601838595}{134217728 \left (2+x \right )}+\frac {9584001347}{8388608 x^{6}}+\frac {6154395725533}{134217728 x^{2}}-\frac {10099142339069}{134217728 x}+\frac {35209}{262144 x^{12}}+\frac {365887609840925}{134217728 \left (2+x \right )^{2}}+\frac {751825061}{8388608 x^{8}}-\frac {647127286119}{33554432 x^{3}}+\frac {1}{65536 x^{16}}-\frac {610621687}{2097152 x^{7}}-\frac {1}{8192 x^{15}}+\frac {73}{32768 x^{14}}-\frac {451}{32768 x^{13}}-\frac {86793}{131072 x^{11}}+\frac {2331487}{524288 x^{10}}-\frac {9314723}{524288 x^{9}}\) \(194\)
risch \(\frac {-524288 x^{31}-13107200 x^{30}-155975680 x^{29}-1167392768 x^{28}-6127091712 x^{27}-23828037632 x^{26}-70774489088 x^{25}-163127910400 x^{24}-293418598400 x^{23}-410371440640 x^{22}-439798726656 x^{21}-349689733120 x^{20}-191661137920 x^{19}-56850415616 x^{18}+6795046912 x^{17}+16583389952 x^{16}+9449846784 x^{15}+3824880640 x^{14}+1425629184 x^{13}+484675072 x^{12}+143786496 x^{11}+45179904 x^{10}+9542400 x^{9}+3159968 x^{8}+397824 x^{7}+160832 x^{6}+9408 x^{5}+5520 x^{4}+96 x^{3}+112 x^{2}+1}{x^{16} \left (x^{16}+32 x^{15}+480 x^{14}+4480 x^{13}+29120 x^{12}+139776 x^{11}+512512 x^{10}+1464320 x^{9}+3294720 x^{8}+5857280 x^{7}+8200192 x^{6}+8945664 x^{5}+7454720 x^{4}+4587520 x^{3}+1966080 x^{2}+524288 x +65536\right )}\) \(237\)
gosper \(-\frac {524288 x^{31}+13107200 x^{30}+155975680 x^{29}+1167392768 x^{28}+6127091712 x^{27}+23828037632 x^{26}+70774489088 x^{25}+163127910400 x^{24}+293418598400 x^{23}+410371440640 x^{22}+439798726656 x^{21}+349689733120 x^{20}+191661137920 x^{19}+56850415616 x^{18}-6795046912 x^{17}-16583389952 x^{16}-9449846784 x^{15}-3824880640 x^{14}-1425629184 x^{13}-484675072 x^{12}-143786496 x^{11}-45179904 x^{10}-9542400 x^{9}-3159968 x^{8}-397824 x^{7}-160832 x^{6}-9408 x^{5}-5520 x^{4}-96 x^{3}-112 x^{2}-1}{x^{16} \left (x^{16}+32 x^{15}+480 x^{14}+4480 x^{13}+29120 x^{12}+139776 x^{11}+512512 x^{10}+1464320 x^{9}+3294720 x^{8}+5857280 x^{7}+8200192 x^{6}+8945664 x^{5}+7454720 x^{4}+4587520 x^{3}+1966080 x^{2}+524288 x +65536\right )}\) \(238\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((524288*x^32+10485760*x^31+100925440*x^30+614203392*x^29+2618032128*x^28+8172208128*x^27+18860670976*x^26+
31082479616*x^25+30720819200*x^24-4145971200*x^23-86671294464*x^22-201710469120*x^21-305923072000*x^20-3540610
08896*x^19-329327366144*x^18-251744145408*x^17-160647395328*x^16-87747545088*x^15-42386477056*x^14-18247276544
*x^13-6896916992*x^12-2431822848*x^11-761634048*x^10-209432832*x^9-60505088*x^8-11342464*x^7-3470656*x^6-36153
6*x^5-135264*x^4-5856*x^3-3136*x^2-32*x-32)/(x^34+34*x^33+544*x^32+5440*x^31+38080*x^30+198016*x^29+792064*x^2
8+2489344*x^27+6223360*x^26+12446720*x^25+19914752*x^24+25346048*x^23+25346048*x^22+19496960*x^21+11141120*x^2
0+4456448*x^19+1114112*x^18+131072*x^17),x,method=_RETURNVERBOSE)

[Out]

(-524288*x^31-13107200*x^30-155975680*x^29-1167392768*x^28-6127091712*x^27-23828037632*x^26-70774489088*x^25-1
63127910400*x^24-293418598400*x^23-410371440640*x^22-439798726656*x^21-349689733120*x^20-191661137920*x^19-568
50415616*x^18+6795046912*x^17+16583389952*x^16+9449846784*x^15+3824880640*x^14+1425629184*x^13+484675072*x^12+
143786496*x^11+45179904*x^10+9542400*x^9+3159968*x^8+397824*x^7+160832*x^6+9408*x^5+5520*x^4+96*x^3+112*x^2+1)
/x^16/(2+x)^16

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maxima [B]  time = 0.36, size = 240, normalized size = 11.43 \begin {gather*} -\frac {524288 \, x^{31} + 13107200 \, x^{30} + 155975680 \, x^{29} + 1167392768 \, x^{28} + 6127091712 \, x^{27} + 23828037632 \, x^{26} + 70774489088 \, x^{25} + 163127910400 \, x^{24} + 293418598400 \, x^{23} + 410371440640 \, x^{22} + 439798726656 \, x^{21} + 349689733120 \, x^{20} + 191661137920 \, x^{19} + 56850415616 \, x^{18} - 6795046912 \, x^{17} - 16583389952 \, x^{16} - 9449846784 \, x^{15} - 3824880640 \, x^{14} - 1425629184 \, x^{13} - 484675072 \, x^{12} - 143786496 \, x^{11} - 45179904 \, x^{10} - 9542400 \, x^{9} - 3159968 \, x^{8} - 397824 \, x^{7} - 160832 \, x^{6} - 9408 \, x^{5} - 5520 \, x^{4} - 96 \, x^{3} - 112 \, x^{2} - 1}{x^{32} + 32 \, x^{31} + 480 \, x^{30} + 4480 \, x^{29} + 29120 \, x^{28} + 139776 \, x^{27} + 512512 \, x^{26} + 1464320 \, x^{25} + 3294720 \, x^{24} + 5857280 \, x^{23} + 8200192 \, x^{22} + 8945664 \, x^{21} + 7454720 \, x^{20} + 4587520 \, x^{19} + 1966080 \, x^{18} + 524288 \, x^{17} + 65536 \, x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((524288*x^32+10485760*x^31+100925440*x^30+614203392*x^29+2618032128*x^28+8172208128*x^27+18860670976
*x^26+31082479616*x^25+30720819200*x^24-4145971200*x^23-86671294464*x^22-201710469120*x^21-305923072000*x^20-3
54061008896*x^19-329327366144*x^18-251744145408*x^17-160647395328*x^16-87747545088*x^15-42386477056*x^14-18247
276544*x^13-6896916992*x^12-2431822848*x^11-761634048*x^10-209432832*x^9-60505088*x^8-11342464*x^7-3470656*x^6
-361536*x^5-135264*x^4-5856*x^3-3136*x^2-32*x-32)/(x^34+34*x^33+544*x^32+5440*x^31+38080*x^30+198016*x^29+7920
64*x^28+2489344*x^27+6223360*x^26+12446720*x^25+19914752*x^24+25346048*x^23+25346048*x^22+19496960*x^21+111411
20*x^20+4456448*x^19+1114112*x^18+131072*x^17),x, algorithm="maxima")

[Out]

-(524288*x^31 + 13107200*x^30 + 155975680*x^29 + 1167392768*x^28 + 6127091712*x^27 + 23828037632*x^26 + 707744
89088*x^25 + 163127910400*x^24 + 293418598400*x^23 + 410371440640*x^22 + 439798726656*x^21 + 349689733120*x^20
 + 191661137920*x^19 + 56850415616*x^18 - 6795046912*x^17 - 16583389952*x^16 - 9449846784*x^15 - 3824880640*x^
14 - 1425629184*x^13 - 484675072*x^12 - 143786496*x^11 - 45179904*x^10 - 9542400*x^9 - 3159968*x^8 - 397824*x^
7 - 160832*x^6 - 9408*x^5 - 5520*x^4 - 96*x^3 - 112*x^2 - 1)/(x^32 + 32*x^31 + 480*x^30 + 4480*x^29 + 29120*x^
28 + 139776*x^27 + 512512*x^26 + 1464320*x^25 + 3294720*x^24 + 5857280*x^23 + 8200192*x^22 + 8945664*x^21 + 74
54720*x^20 + 4587520*x^19 + 1966080*x^18 + 524288*x^17 + 65536*x^16)

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mupad [B]  time = 1.93, size = 239, normalized size = 11.38 \begin {gather*} \frac {-524288\,x^{31}-13107200\,x^{30}-155975680\,x^{29}-1167392768\,x^{28}-6127091712\,x^{27}-23828037632\,x^{26}-70774489088\,x^{25}-163127910400\,x^{24}-293418598400\,x^{23}-410371440640\,x^{22}-439798726656\,x^{21}-349689733120\,x^{20}-191661137920\,x^{19}-56850415616\,x^{18}+6795046912\,x^{17}+16583389952\,x^{16}+9449846784\,x^{15}+3824880640\,x^{14}+1425629184\,x^{13}+484675072\,x^{12}+143786496\,x^{11}+45179904\,x^{10}+9542400\,x^9+3159968\,x^8+397824\,x^7+160832\,x^6+9408\,x^5+5520\,x^4+96\,x^3+112\,x^2+1}{x^{32}+32\,x^{31}+480\,x^{30}+4480\,x^{29}+29120\,x^{28}+139776\,x^{27}+512512\,x^{26}+1464320\,x^{25}+3294720\,x^{24}+5857280\,x^{23}+8200192\,x^{22}+8945664\,x^{21}+7454720\,x^{20}+4587520\,x^{19}+1966080\,x^{18}+524288\,x^{17}+65536\,x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(32*x + 3136*x^2 + 5856*x^3 + 135264*x^4 + 361536*x^5 + 3470656*x^6 + 11342464*x^7 + 60505088*x^8 + 20943
2832*x^9 + 761634048*x^10 + 2431822848*x^11 + 6896916992*x^12 + 18247276544*x^13 + 42386477056*x^14 + 87747545
088*x^15 + 160647395328*x^16 + 251744145408*x^17 + 329327366144*x^18 + 354061008896*x^19 + 305923072000*x^20 +
 201710469120*x^21 + 86671294464*x^22 + 4145971200*x^23 - 30720819200*x^24 - 31082479616*x^25 - 18860670976*x^
26 - 8172208128*x^27 - 2618032128*x^28 - 614203392*x^29 - 100925440*x^30 - 10485760*x^31 - 524288*x^32 + 32)/(
131072*x^17 + 1114112*x^18 + 4456448*x^19 + 11141120*x^20 + 19496960*x^21 + 25346048*x^22 + 25346048*x^23 + 19
914752*x^24 + 12446720*x^25 + 6223360*x^26 + 2489344*x^27 + 792064*x^28 + 198016*x^29 + 38080*x^30 + 5440*x^31
 + 544*x^32 + 34*x^33 + x^34),x)

[Out]

(112*x^2 + 96*x^3 + 5520*x^4 + 9408*x^5 + 160832*x^6 + 397824*x^7 + 3159968*x^8 + 9542400*x^9 + 45179904*x^10
+ 143786496*x^11 + 484675072*x^12 + 1425629184*x^13 + 3824880640*x^14 + 9449846784*x^15 + 16583389952*x^16 + 6
795046912*x^17 - 56850415616*x^18 - 191661137920*x^19 - 349689733120*x^20 - 439798726656*x^21 - 410371440640*x
^22 - 293418598400*x^23 - 163127910400*x^24 - 70774489088*x^25 - 23828037632*x^26 - 6127091712*x^27 - 11673927
68*x^28 - 155975680*x^29 - 13107200*x^30 - 524288*x^31 + 1)/(65536*x^16 + 524288*x^17 + 1966080*x^18 + 4587520
*x^19 + 7454720*x^20 + 8945664*x^21 + 8200192*x^22 + 5857280*x^23 + 3294720*x^24 + 1464320*x^25 + 512512*x^26
+ 139776*x^27 + 29120*x^28 + 4480*x^29 + 480*x^30 + 32*x^31 + x^32)

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sympy [B]  time = 0.52, size = 238, normalized size = 11.33 \begin {gather*} \frac {- 524288 x^{31} - 13107200 x^{30} - 155975680 x^{29} - 1167392768 x^{28} - 6127091712 x^{27} - 23828037632 x^{26} - 70774489088 x^{25} - 163127910400 x^{24} - 293418598400 x^{23} - 410371440640 x^{22} - 439798726656 x^{21} - 349689733120 x^{20} - 191661137920 x^{19} - 56850415616 x^{18} + 6795046912 x^{17} + 16583389952 x^{16} + 9449846784 x^{15} + 3824880640 x^{14} + 1425629184 x^{13} + 484675072 x^{12} + 143786496 x^{11} + 45179904 x^{10} + 9542400 x^{9} + 3159968 x^{8} + 397824 x^{7} + 160832 x^{6} + 9408 x^{5} + 5520 x^{4} + 96 x^{3} + 112 x^{2} + 1}{x^{32} + 32 x^{31} + 480 x^{30} + 4480 x^{29} + 29120 x^{28} + 139776 x^{27} + 512512 x^{26} + 1464320 x^{25} + 3294720 x^{24} + 5857280 x^{23} + 8200192 x^{22} + 8945664 x^{21} + 7454720 x^{20} + 4587520 x^{19} + 1966080 x^{18} + 524288 x^{17} + 65536 x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((524288*x**32+10485760*x**31+100925440*x**30+614203392*x**29+2618032128*x**28+8172208128*x**27+18860
670976*x**26+31082479616*x**25+30720819200*x**24-4145971200*x**23-86671294464*x**22-201710469120*x**21-3059230
72000*x**20-354061008896*x**19-329327366144*x**18-251744145408*x**17-160647395328*x**16-87747545088*x**15-4238
6477056*x**14-18247276544*x**13-6896916992*x**12-2431822848*x**11-761634048*x**10-209432832*x**9-60505088*x**8
-11342464*x**7-3470656*x**6-361536*x**5-135264*x**4-5856*x**3-3136*x**2-32*x-32)/(x**34+34*x**33+544*x**32+544
0*x**31+38080*x**30+198016*x**29+792064*x**28+2489344*x**27+6223360*x**26+12446720*x**25+19914752*x**24+253460
48*x**23+25346048*x**22+19496960*x**21+11141120*x**20+4456448*x**19+1114112*x**18+131072*x**17),x)

[Out]

(-524288*x**31 - 13107200*x**30 - 155975680*x**29 - 1167392768*x**28 - 6127091712*x**27 - 23828037632*x**26 -
70774489088*x**25 - 163127910400*x**24 - 293418598400*x**23 - 410371440640*x**22 - 439798726656*x**21 - 349689
733120*x**20 - 191661137920*x**19 - 56850415616*x**18 + 6795046912*x**17 + 16583389952*x**16 + 9449846784*x**1
5 + 3824880640*x**14 + 1425629184*x**13 + 484675072*x**12 + 143786496*x**11 + 45179904*x**10 + 9542400*x**9 +
3159968*x**8 + 397824*x**7 + 160832*x**6 + 9408*x**5 + 5520*x**4 + 96*x**3 + 112*x**2 + 1)/(x**32 + 32*x**31 +
 480*x**30 + 4480*x**29 + 29120*x**28 + 139776*x**27 + 512512*x**26 + 1464320*x**25 + 3294720*x**24 + 5857280*
x**23 + 8200192*x**22 + 8945664*x**21 + 7454720*x**20 + 4587520*x**19 + 1966080*x**18 + 524288*x**17 + 65536*x
**16)

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