3.31.91 \(\int \frac {(20503125000 x^7+18452812500 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}[phone] x^{15}[phone] x^{16}[phone] x^{17}[phone] x^{18}[phone] x^{19}[phone] x^{20}[phone] x^{21}[phone] x^{22}[phone] x^{23}[phone] x^{24}} \, dx\)

Optimal. Leaf size=26 \[ \frac {\log (2)}{-3-x+\left (3+x+\left (\frac {25}{9 x^2}+x\right )^2\right )^2} \]

________________________________________________________________________________________

Rubi [F]  time = 7.23, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (20503125000 x^7+18452812500 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}[phone] x^{15}[phone] x^{16}[phone] x^{17}[phone] x^{18}[phone] x^{19}[phone] x^{20}[phone] x^{21}[phone] x^{22}[phone] x^{23}[phone] x^{24}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 1992903750*x^12 + 3985807500*x^13 + 1434890700*x^
14 - 693530505*x^16 - 602654094*x^17 - 258280326*x^18 - 172186884*x^19)*Log[2])/(152587890625 + 439453125000*x
^3 + 237304687500*x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125000*x^7 + 293878125000*x^8 + 48581015625
0*x^9 + 476697656250*x^10 + 330920437500*x^11 + 328796313750*x^12 + 271477777500*x^13 + 180099450000*x^14 + 13
7973893400*x^15 + 93382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 15525517374*x^19 + 6356565801*x^20
+ 2592369198*x^21 + 774840978*x^22 + 172186884*x^23 + 43046721*x^24),x]

[Out]

(1282743*Log[2])/(2*(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 10
5705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)) + 95206640625*Log[2]*Defer[Int][(390625 + 562500*x^3 + 303750
*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^(
-2), x] - 652018359375*Log[2]*Defer[Int][x/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 21870
0*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] + 1092850734375*Log[2]*Defer[Int]
[x^2/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 4592
7*x^10 + 13122*x^11 + 6561*x^12)^2, x] + 1076402216250*Log[2]*Defer[Int][x^3/(390625 + 562500*x^3 + 303750*x^4
+ 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x]
- 576914197500*Log[2]*Defer[Int][x^4/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7
+ 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] + 676111050000*Log[2]*Defer[Int][x^5/(
390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10
+ 13122*x^11 + 6561*x^12)^2, x] + 1120427546850*Log[2]*Defer[Int][x^6/(390625 + 562500*x^3 + 303750*x^4 + 101
250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] + 227
361167352*Log[2]*Defer[Int][x^7/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112
266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] + (513371238363*Log[2]*Defer[Int][x^8/(39062
5 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13
122*x^11 + 6561*x^12)^2, x])/2 + 226448309178*Log[2]*Defer[Int][x^9/(390625 + 562500*x^3 + 303750*x^4 + 101250
*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] + 139816
81269*Log[2]*Defer[Int][x^10/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266
*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)^2, x] - 243729*Log[2]*Defer[Int][(390625 + 562500*x^3
+ 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 656
1*x^12)^(-1), x] + 1669167*Log[2]*Defer[Int][x/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 2
18700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12), x] - 26973*Log[2]*Defer[Int][x^2/(
390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10
+ 13122*x^11 + 6561*x^12), x] - 409698*Log[2]*Defer[Int][x^3/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 +
303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12), x] + 94041*Log[2]*D
efer[Int][x^4/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x
^9 + 45927*x^10 + 13122*x^11 + 6561*x^12), x] + 65610*Log[2]*Defer[Int][x^5/(390625 + 562500*x^3 + 303750*x^4
+ 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12), x] +
13122*Log[2]*Defer[Int][x^6/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*
x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12), x] - 26244*Log[2]*Defer[Int][x^7/(390625 + 562500*x^3
+ 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 656
1*x^12), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log (2) \int \frac {20503125000 x^7+18452812500 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}[phone] x^{15}[phone] x^{16}[phone] x^{17}[phone] x^{18}[phone] x^{19}[phone] x^{20}[phone] x^{21}[phone] x^{22}[phone] x^{23}[phone] x^{24}} \, dx\\ &=\log (2) \int \left (-\frac {243 \left (-391796875+2683203125 x-43359375 x^2-1222781250 x^3+3710323125 x^4+2027936250 x^5-570172500 x^6+1434866400 x^7+1454650002 x^8+280306089 x^9+323436888 x^{10}[phone] x^{11}\right )}{\left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )^2}-\frac {243 \left (1003-6869 x+111 x^2+1686 x^3-387 x^4-270 x^5-54 x^6+108 x^7\right )}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}\right ) \, dx\\ &=-\left ((243 \log (2)) \int \frac {-391796875+2683203125 x-43359375 x^2-1222781250 x^3+3710323125 x^4+2027936250 x^5-570172500 x^6+1434866400 x^7+1454650002 x^8+280306089 x^9+323436888 x^{10}[phone] x^{11}}{\left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )^2} \, dx\right )-(243 \log (2)) \int \frac {1003-6869 x+111 x^2+1686 x^3-387 x^4-270 x^5-54 x^6+108 x^7}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx\\ &=\frac {1282743 \log (2)}{2 \left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )}-\frac {1}{324} \log (2) \int \frac {-30846951562500+211253948437500 x-354083637937500 x^2-348754318065000 x^3+186920199990000 x^4-219059980200000 x^5-363018525179400 x^6-73665018222048 x^7-83166140614806 x^8-73369252173672 x^9-4530064731156 x^{10}}{\left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )^2} \, dx-(243 \log (2)) \int \left (\frac {1003}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}-\frac {6869 x}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}+\frac {111 x^2}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}+\frac {1686 x^3}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}-\frac {387 x^4}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}-\frac {270 x^5}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}-\frac {54 x^6}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}+\frac {108 x^7}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}}\right ) \, dx\\ &=\frac {1282743 \log (2)}{2 \left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )}-\frac {1}{324} \log (2) \int \frac {39366 \left (-783593750+5366406250 x-8994656250 x^2-8859277500 x^3+4748265000 x^4-5564700000 x^5-9221625900 x^6-1871285328 x^7-2112638841 x^8-1863772092 x^9-115075566 x^{10}\right )}{\left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )^2} \, dx+(13122 \log (2)) \int \frac {x^6}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(26244 \log (2)) \int \frac {x^7}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(26973 \log (2)) \int \frac {x^2}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(65610 \log (2)) \int \frac {x^5}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(94041 \log (2)) \int \frac {x^4}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(243729 \log (2)) \int \frac {1}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(409698 \log (2)) \int \frac {x^3}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(1669167 \log (2)) \int \frac {x}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx\\ &=\frac {1282743 \log (2)}{2 \left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )}-\frac {1}{2} (243 \log (2)) \int \frac {-783593750+5366406250 x-8994656250 x^2-8859277500 x^3+4748265000 x^4-5564700000 x^5-9221625900 x^6-1871285328 x^7-2112638841 x^8-1863772092 x^9-115075566 x^{10}}{\left (390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}\right )^2} \, dx+(13122 \log (2)) \int \frac {x^6}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(26244 \log (2)) \int \frac {x^7}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(26973 \log (2)) \int \frac {x^2}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(65610 \log (2)) \int \frac {x^5}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(94041 \log (2)) \int \frac {x^4}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(243729 \log (2)) \int \frac {1}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx-(409698 \log (2)) \int \frac {x^3}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx+(1669167 \log (2)) \int \frac {x}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.04, size = 61, normalized size = 2.35 \begin {gather*} \frac {6561 x^8 \log (2)}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 1992903750*x^12 + 3985807500*x^13 + 1434890
700*x^14 - 693530505*x^16 - 602654094*x^17 - 258280326*x^18 - 172186884*x^19)*Log[2])/(152587890625 + 43945312
5000*x^3 + 237304687500*x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125000*x^7 + 293878125000*x^8 + 48581
0156250*x^9 + 476697656250*x^10 + 330920437500*x^11 + 328796313750*x^12 + 271477777500*x^13 + 180099450000*x^1
4 + 137973893400*x^15 + 93382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 15525517374*x^19 + 6356565801
*x^20 + 2592369198*x^21 + 774840978*x^22 + 172186884*x^23 + 43046721*x^24),x]

[Out]

(6561*x^8*Log[2])/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 1057
05*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12)

________________________________________________________________________________________

fricas [B]  time = 0.56, size = 61, normalized size = 2.35 \begin {gather*} \frac {6561 \, x^{8} \log \relax (2)}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+1434890700*x^14+3985807500*x^13+199290
3750*x^12+7971615000*x^11+18452812500*x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^2
2+2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^17+93382686756*x^16+13797389
3400*x^15+180099450000*x^14+271477777500*x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+4858101562
50*x^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+237304687500*x^4+439453125000*x^3+15
2587890625),x, algorithm="fricas")

[Out]

6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266*x^8 + 218700*x^7 + 303750*x^6 + 101
250*x^5 + 303750*x^4 + 562500*x^3 + 390625)

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giac [B]  time = 0.28, size = 61, normalized size = 2.35 \begin {gather*} \frac {6561 \, x^{8} \log \relax (2)}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+1434890700*x^14+3985807500*x^13+199290
3750*x^12+7971615000*x^11+18452812500*x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^2
2+2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^17+93382686756*x^16+13797389
3400*x^15+180099450000*x^14+271477777500*x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+4858101562
50*x^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+237304687500*x^4+439453125000*x^3+15
2587890625),x, algorithm="giac")

[Out]

6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266*x^8 + 218700*x^7 + 303750*x^6 + 101
250*x^5 + 303750*x^4 + 562500*x^3 + 390625)

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maple [B]  time = 0.15, size = 59, normalized size = 2.27

method	result	size
default	\(\frac {\ln \relax (2) x^{8}}{x^{12}+2 x^{11}+7 x^{10}+\frac {145}{9} x^{9}+\frac {154}{9} x^{8}+\frac {100}{3} x^{7}+\frac {1250}{27} x^{6}+\frac {1250}{81} x^{5}+\frac {1250}{27} x^{4}+\frac {62500}{729} x^{3}+\frac {390625}{6561}}\)	\(59\)
risch	\(\frac {\ln \relax (2) x^{8}}{x^{12}+2 x^{11}+7 x^{10}+\frac {145}{9} x^{9}+\frac {154}{9} x^{8}+\frac {100}{3} x^{7}+\frac {1250}{27} x^{6}+\frac {1250}{81} x^{5}+\frac {1250}{27} x^{4}+\frac {62500}{729} x^{3}+\frac {390625}{6561}}\)	\(59\)
gosper	\(\frac {6561 x^{8} \ln \relax (2)}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625}\)	\(62\)
norman	\(\frac {6561 x^{8} \ln \relax (2)}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625}\)	\(62\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+1434890700*x^14+3985807500*x^13+1992903750*x
^12+7971615000*x^11+18452812500*x^10+20503125000*x^7)*ln(2)/(43046721*x^24+172186884*x^23+774840978*x^22+25923
69198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^17+93382686756*x^16+137973893400*x^
15+180099450000*x^14+271477777500*x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x^9+
293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+237304687500*x^4+439453125000*x^3+152587890
625),x,method=_RETURNVERBOSE)

[Out]

ln(2)*x^8/(x^12+2*x^11+7*x^10+145/9*x^9+154/9*x^8+100/3*x^7+1250/27*x^6+1250/81*x^5+1250/27*x^4+62500/729*x^3+
390625/6561)

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maxima [B]  time = 0.36, size = 61, normalized size = 2.35 \begin {gather*} \frac {6561 \, x^{8} \log \relax (2)}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+1434890700*x^14+3985807500*x^13+199290
3750*x^12+7971615000*x^11+18452812500*x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^2
2+2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^17+93382686756*x^16+13797389
3400*x^15+180099450000*x^14+271477777500*x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+4858101562
50*x^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+237304687500*x^4+439453125000*x^3+15
2587890625),x, algorithm="maxima")

[Out]

6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266*x^8 + 218700*x^7 + 303750*x^6 + 101
250*x^5 + 303750*x^4 + 562500*x^3 + 390625)

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mupad [B]  time = 1.95, size = 61, normalized size = 2.35 \begin {gather*} \frac {6561\,x^8\,\ln \relax (2)}{6561\,x^{12}+13122\,x^{11}+45927\,x^{10}+105705\,x^9+112266\,x^8+218700\,x^7+303750\,x^6+101250\,x^5+303750\,x^4+562500\,x^3+390625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2)*(20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 1992903750*x^12 + 3985807500*x^13 + 143489
0700*x^14 - 693530505*x^16 - 602654094*x^17 - 258280326*x^18 - 172186884*x^19))/(439453125000*x^3 + 2373046875
00*x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125000*x^7 + 293878125000*x^8 + 485810156250*x^9 + 4766976
56250*x^10 + 330920437500*x^11 + 328796313750*x^12 + 271477777500*x^13 + 180099450000*x^14 + 137973893400*x^15
+ 93382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 15525517374*x^19 + 6356565801*x^20 + 2592369198*x^
21 + 774840978*x^22 + 172186884*x^23 + 43046721*x^24 + 152587890625),x)

[Out]

(6561*x^8*log(2))/(562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 +
45927*x^10 + 13122*x^11 + 6561*x^12 + 390625)

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sympy [B]  time = 2.78, size = 60, normalized size = 2.31 \begin {gather*} \frac {6561 x^{8} \log {\relax (2 )}}{6561 x^{12} + 13122 x^{11} + 45927 x^{10} + 105705 x^{9} + 112266 x^{8} + 218700 x^{7} + 303750 x^{6} + 101250 x^{5} + 303750 x^{4} + 562500 x^{3} + 390625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-172186884*x**19-258280326*x**18-602654094*x**17-693530505*x**16+1434890700*x**14+3985807500*x**13+
1992903750*x**12+7971615000*x**11+18452812500*x**10+20503125000*x**7)*ln(2)/(43046721*x**24+172186884*x**23+77
4840978*x**22+2592369198*x**21+6356565801*x**20+15525517374*x**19+31210998489*x**18+53122842360*x**17+93382686
756*x**16+137973893400*x**15+180099450000*x**14+271477777500*x**13+328796313750*x**12+330920437500*x**11+47669
7656250*x**10+485810156250*x**9+293878125000*x**8+512578125000*x**7+553710937500*x**6+79101562500*x**5+2373046
87500*x**4+439453125000*x**3+152587890625),x)

[Out]

6561*x**8*log(2)/(6561*x**12 + 13122*x**11 + 45927*x**10 + 105705*x**9 + 112266*x**8 + 218700*x**7 + 303750*x*
*6 + 101250*x**5 + 303750*x**4 + 562500*x**3 + 390625)

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