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 = 0.10, antiderivative size = 56, normalized size of antiderivative = 1.00, 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 611
Rule 1352
Rule 1390
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*}
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Mathematica [B] time = 0.01, 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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fricas [B] time = 0.66, size = 174, normalized size = 3.11 \[ \frac {16677181699666569}{35} x^{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac {101849676181562048256}{5} x^{30} + 67899784121041365504 x^{29} + \frac {2625458326972530284475}{14} x^{28} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac {7584660010542711771792}{5} x^{25} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac {26506949038858918036881}{7} x^{21} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac {17344958593049772048}{5} x^{10} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac {4057390785756924}{5} x^{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.42, size = 46, normalized size = 0.82 \[ \frac {1}{105} \, {\left (3 \, x + 2\right )}^{35} + \frac {1}{42} \, {\left (3 \, x + 2\right )}^{28} + \frac {1}{21} \, {\left (3 \, x + 2\right )}^{21} + \frac {1}{21} \, {\left (3 \, x + 2\right )}^{14} + \frac {1}{21} \, {\left (3 \, x + 2\right )}^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 175, normalized size = 3.12 \[ \frac {16677181699666569}{35} x^{35}+11118121133111046 x^{34}+126005372841925188 x^{33}+924039400840784712 x^{32}+4928210137817518464 x^{31}+\frac {101849676181562048256}{5} x^{30}+67899784121041365504 x^{29}+\frac {2625458326972530284475}{14} x^{28}+437576396725285446564 x^{27}+875152864622814086340 x^{26}+\frac {7584660010542711771792}{5} x^{25}+2298383223254096766840 x^{24}+3064515076512846852480 x^{23}+3614565944605222108800 x^{22}+\frac {26506949038858918036881}{7} x^{21}+3534290697929473864098 x^{20}+2945285062308448290360 x^{19}+2194577166014752240080 x^{18}+1463104032160519033200 x^{17}+872775774067455498528 x^{16}+465517091041681015296 x^{15}+221699757548270194389 x^{14}+94069263918929616324 x^{13}+35454069480572048124 x^{12}+11821487501620716192 x^{11}+\frac {17344958593049772048}{5} x^{10}+889942562270387136 x^{9}+197897276851452864 x^{8}+37727143432895007 x^{7}+6077684727888102 x^{6}+\frac {4057390785756924}{5} x^{5}+87406679578680 x^{4}+7299544818384 x^{3}+443569828128 x^{2}+17451466816 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.77, size = 174, normalized size = 3.11 \[ \frac {16677181699666569}{35} \, x^{35} + 11118121133111046 \, x^{34} + 126005372841925188 \, x^{33} + 924039400840784712 \, x^{32} + 4928210137817518464 \, x^{31} + \frac {101849676181562048256}{5} \, x^{30} + 67899784121041365504 \, x^{29} + \frac {2625458326972530284475}{14} \, x^{28} + 437576396725285446564 \, x^{27} + 875152864622814086340 \, x^{26} + \frac {7584660010542711771792}{5} \, x^{25} + 2298383223254096766840 \, x^{24} + 3064515076512846852480 \, x^{23} + 3614565944605222108800 \, x^{22} + \frac {26506949038858918036881}{7} \, x^{21} + 3534290697929473864098 \, x^{20} + 2945285062308448290360 \, x^{19} + 2194577166014752240080 \, x^{18} + 1463104032160519033200 \, x^{17} + 872775774067455498528 \, x^{16} + 465517091041681015296 \, x^{15} + 221699757548270194389 \, x^{14} + 94069263918929616324 \, x^{13} + 35454069480572048124 \, x^{12} + 11821487501620716192 \, x^{11} + \frac {17344958593049772048}{5} \, x^{10} + 889942562270387136 \, x^{9} + 197897276851452864 \, x^{8} + 37727143432895007 \, x^{7} + 6077684727888102 \, x^{6} + \frac {4057390785756924}{5} \, x^{5} + 87406679578680 \, x^{4} + 7299544818384 \, x^{3} + 443569828128 \, x^{2} + 17451466816 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.60, size = 46, normalized size = 0.82 \[ \frac {{\left (3\,x+2\right )}^7}{21}+\frac {{\left (3\,x+2\right )}^{14}}{21}+\frac {{\left (3\,x+2\right )}^{21}}{21}+\frac {{\left (3\,x+2\right )}^{28}}{42}+\frac {{\left (3\,x+2\right )}^{35}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.15, size = 187, normalized size = 3.34 \[ \frac {16677181699666569 x^{35}}{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac {101849676181562048256 x^{30}}{5} + 67899784121041365504 x^{29} + \frac {2625458326972530284475 x^{28}}{14} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac {7584660010542711771792 x^{25}}{5} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac {26506949038858918036881 x^{21}}{7} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac {17344958593049772048 x^{10}}{5} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac {4057390785756924 x^{5}}{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x \]
Verification of antiderivative is not currently implemented for this CAS.
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