Optimal. Leaf size=56 \[ \frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]
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Rubi [A] time = 0.0957482, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.115, Rules used = {1390, 1352, 611} \[ \frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 1390
Rule 1352
Rule 611
Rubi steps
\begin{align*} \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right )^2 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^6 \left (1+x^7+x^{14}\right )^2 \, dx,x,2+3 x\right )\\ &=\frac{1}{21} \operatorname{Subst}\left (\int \left (1+x+x^2\right )^2 \, dx,x,(2+3 x)^7\right )\\ &=\frac{1}{21} \operatorname{Subst}\left (\int \left (1+2 x+3 x^2+2 x^3+x^4\right ) \, dx,x,(2+3 x)^7\right )\\ &=\frac{1}{21} (2+3 x)^7+\frac{1}{21} (2+3 x)^{14}+\frac{1}{21} (2+3 x)^{21}+\frac{1}{42} (2+3 x)^{28}+\frac{1}{105} (2+3 x)^{35}\\ \end{align*}
Mathematica [B] time = 0.0116218, size = 188, normalized size = 3.36 \[ \frac{16677181699666569 x^{35}}{35}+11118121133111046 x^{34}+126005372841925188 x^{33}+924039400840784712 x^{32}+4928210137817518464 x^{31}+\frac{101849676181562048256 x^{30}}{5}+67899784121041365504 x^{29}+\frac{2625458326972530284475 x^{28}}{14}+437576396725285446564 x^{27}+875152864622814086340 x^{26}+\frac{7584660010542711771792 x^{25}}{5}+2298383223254096766840 x^{24}+3064515076512846852480 x^{23}+3614565944605222108800 x^{22}+\frac{26506949038858918036881 x^{21}}{7}+3534290697929473864098 x^{20}+2945285062308448290360 x^{19}+2194577166014752240080 x^{18}+1463104032160519033200 x^{17}+872775774067455498528 x^{16}+465517091041681015296 x^{15}+221699757548270194389 x^{14}+94069263918929616324 x^{13}+35454069480572048124 x^{12}+11821487501620716192 x^{11}+\frac{17344958593049772048 x^{10}}{5}+889942562270387136 x^9+197897276851452864 x^8+37727143432895007 x^7+6077684727888102 x^6+\frac{4057390785756924 x^5}{5}+87406679578680 x^4+7299544818384 x^3+443569828128 x^2+17451466816 x \]
Antiderivative was successfully verified.
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Maple [B] time = 0.003, size = 175, normalized size = 3.1 \begin{align*} 17451466816\,x+11118121133111046\,{x}^{34}+126005372841925188\,{x}^{33}+924039400840784712\,{x}^{32}+4928210137817518464\,{x}^{31}+{\frac{101849676181562048256\,{x}^{30}}{5}}+67899784121041365504\,{x}^{29}+{\frac{2625458326972530284475\,{x}^{28}}{14}}+437576396725285446564\,{x}^{27}+875152864622814086340\,{x}^{26}+{\frac{7584660010542711771792\,{x}^{25}}{5}}+2298383223254096766840\,{x}^{24}+3064515076512846852480\,{x}^{23}+3614565944605222108800\,{x}^{22}+{\frac{26506949038858918036881\,{x}^{21}}{7}}+3534290697929473864098\,{x}^{20}+2945285062308448290360\,{x}^{19}+2194577166014752240080\,{x}^{18}+1463104032160519033200\,{x}^{17}+872775774067455498528\,{x}^{16}+465517091041681015296\,{x}^{15}+{\frac{17344958593049772048\,{x}^{10}}{5}}+197897276851452864\,{x}^{8}+37727143432895007\,{x}^{7}+221699757548270194389\,{x}^{14}+11821487501620716192\,{x}^{11}+94069263918929616324\,{x}^{13}+35454069480572048124\,{x}^{12}+889942562270387136\,{x}^{9}+7299544818384\,{x}^{3}+6077684727888102\,{x}^{6}+{\frac{4057390785756924\,{x}^{5}}{5}}+443569828128\,{x}^{2}+87406679578680\,{x}^{4}+{\frac{16677181699666569\,{x}^{35}}{35}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01913, size = 235, normalized size = 4.2 \begin{align*} \frac{16677181699666569}{35} \, x^{35} + 11118121133111046 \, x^{34} + 126005372841925188 \, x^{33} + 924039400840784712 \, x^{32} + 4928210137817518464 \, x^{31} + \frac{101849676181562048256}{5} \, x^{30} + 67899784121041365504 \, x^{29} + \frac{2625458326972530284475}{14} \, x^{28} + 437576396725285446564 \, x^{27} + 875152864622814086340 \, x^{26} + \frac{7584660010542711771792}{5} \, x^{25} + 2298383223254096766840 \, x^{24} + 3064515076512846852480 \, x^{23} + 3614565944605222108800 \, x^{22} + \frac{26506949038858918036881}{7} \, x^{21} + 3534290697929473864098 \, x^{20} + 2945285062308448290360 \, x^{19} + 2194577166014752240080 \, x^{18} + 1463104032160519033200 \, x^{17} + 872775774067455498528 \, x^{16} + 465517091041681015296 \, x^{15} + 221699757548270194389 \, x^{14} + 94069263918929616324 \, x^{13} + 35454069480572048124 \, x^{12} + 11821487501620716192 \, x^{11} + \frac{17344958593049772048}{5} \, x^{10} + 889942562270387136 \, x^{9} + 197897276851452864 \, x^{8} + 37727143432895007 \, x^{7} + 6077684727888102 \, x^{6} + \frac{4057390785756924}{5} \, x^{5} + 87406679578680 \, x^{4} + 7299544818384 \, x^{3} + 443569828128 \, x^{2} + 17451466816 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.00882, size = 1289, normalized size = 23.02 \begin{align*} \frac{16677181699666569}{35} x^{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac{101849676181562048256}{5} x^{30} + 67899784121041365504 x^{29} + \frac{2625458326972530284475}{14} x^{28} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac{7584660010542711771792}{5} x^{25} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac{26506949038858918036881}{7} x^{21} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac{17344958593049772048}{5} x^{10} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac{4057390785756924}{5} x^{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.134396, size = 187, normalized size = 3.34 \begin{align*} \frac{16677181699666569 x^{35}}{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac{101849676181562048256 x^{30}}{5} + 67899784121041365504 x^{29} + \frac{2625458326972530284475 x^{28}}{14} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac{7584660010542711771792 x^{25}}{5} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac{26506949038858918036881 x^{21}}{7} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac{17344958593049772048 x^{10}}{5} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac{4057390785756924 x^{5}}{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10208, size = 62, normalized size = 1.11 \begin{align*} \frac{1}{105} \,{\left (3 \, x + 2\right )}^{35} + \frac{1}{42} \,{\left (3 \, x + 2\right )}^{28} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{21} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{14} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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