3.664 \(\int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right )^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]

[Out]

(2 + 3*x)^7/21 + (2 + 3*x)^14/21 + (2 + 3*x)^21/21 + (2 + 3*x)^28/42 + (2 + 3*x)
^35/105

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Rubi [A]  time = 0.190905, 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 \[ \frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14)^2,x]

[Out]

(2 + 3*x)^7/21 + (2 + 3*x)^14/21 + (2 + 3*x)^21/21 + (2 + 3*x)^28/42 + (2 + 3*x)
^35/105

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\left (3 x + 2\right )^{35}}{105} + \frac{\left (3 x + 2\right )^{28}}{42} + \frac{\left (3 x + 2\right )^{21}}{21} + \frac{\left (3 x + 2\right )^{7}}{21} + \frac{2 \int ^{\left (3 x + 2\right )^{7}} x\, dx}{21} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14)**2,x)

[Out]

(3*x + 2)**35/105 + (3*x + 2)**28/42 + (3*x + 2)**21/21 + (3*x + 2)**7/21 + 2*In
tegral(x, (x, (3*x + 2)**7))/21

_______________________________________________________________________________________

Mathematica [B]  time = 0.0124685, size = 188, normalized size = 3.36 \[ \frac{16677181699666569 x^{35}}{35}+11118121133111046 x^{34}+126005372841925188 x^{33}+924039400840784712 x^{32}+4928210137817518464 x^{31}+\frac{101849676181562048256 x^{30}}{5}+67899784121041365504 x^{29}+\frac{2625458326972530284475 x^{28}}{14}+437576396725285446564 x^{27}+875152864622814086340 x^{26}+\frac{7584660010542711771792 x^{25}}{5}+2298383223254096766840 x^{24}+3064515076512846852480 x^{23}+3614565944605222108800 x^{22}+\frac{26506949038858918036881 x^{21}}{7}+3534290697929473864098 x^{20}+2945285062308448290360 x^{19}+2194577166014752240080 x^{18}+1463104032160519033200 x^{17}+872775774067455498528 x^{16}+465517091041681015296 x^{15}+221699757548270194389 x^{14}+94069263918929616324 x^{13}+35454069480572048124 x^{12}+11821487501620716192 x^{11}+\frac{17344958593049772048 x^{10}}{5}+889942562270387136 x^9+197897276851452864 x^8+37727143432895007 x^7+6077684727888102 x^6+\frac{4057390785756924 x^5}{5}[phone] x^4+7299544818384 x^3+443569828128 x^2+17451466816 x \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14)^2,x]

[Out]

17451466816*x + 443569828128*x^2 + 7299544818384*x^3 + 87406679578680*x^4 + (405
7390785756924*x^5)/5 + 6077684727888102*x^6 + 37727143432895007*x^7 + 1978972768
51452864*x^8 + 889942562270387136*x^9 + (17344958593049772048*x^10)/5 + 11821487
501620716192*x^11 + 35454069480572048124*x^12 + 94069263918929616324*x^13 + 2216
99757548270194389*x^14 + 465517091041681015296*x^15 + 872775774067455498528*x^16
+ 1463104032160519033200*x^17 + 2194577166014752240080*x^18 + 29452850623084482
90360*x^19 + 3534290697929473864098*x^20 + (26506949038858918036881*x^21)/7 + 36
14565944605222108800*x^22 + 3064515076512846852480*x^23 + 2298383223254096766840
*x^24 + (7584660010542711771792*x^25)/5 + 875152864622814086340*x^26 + 437576396
725285446564*x^27 + (2625458326972530284475*x^28)/14 + 67899784121041365504*x^29
+ (101849676181562048256*x^30)/5 + 4928210137817518464*x^31 + 92403940084078471
2*x^32 + 126005372841925188*x^33 + 11118121133111046*x^34 + (16677181699666569*x
^35)/35

_______________________________________________________________________________________

Maple [B]  time = 0.005, size = 175, normalized size = 3.1 \[ 17451466816\,x+3534290697929473864098\,{x}^{20}+2194577166014752240080\,{x}^{18}+2945285062308448290360\,{x}^{19}+{\frac{26506949038858918036881\,{x}^{21}}{7}}+{\frac{2625458326972530284475\,{x}^{28}}{14}}+2298383223254096766840\,{x}^{24}+875152864622814086340\,{x}^{26}[phone]\,{x}^{2}[phone]\,{x}^{4}+{\frac{4057390785756924\,{x}^{5}}{5}}[phone]\,{x}^{3}+{\frac{16677181699666569\,{x}^{35}}{35}}+4928210137817518464\,{x}^{31}+{\frac{101849676181562048256\,{x}^{30}}{5}}+67899784121041365504\,{x}^{29}+11118121133111046\,{x}^{34}+126005372841925188\,{x}^{33}+924039400840784712\,{x}^{32}+1463104032160519033200\,{x}^{17}+872775774067455498528\,{x}^{16}+197897276851452864\,{x}^{8}+6077684727888102\,{x}^{6}+221699757548270194389\,{x}^{14}+465517091041681015296\,{x}^{15}+889942562270387136\,{x}^{9}+{\frac{17344958593049772048\,{x}^{10}}{5}}+11821487501620716192\,{x}^{11}+35454069480572048124\,{x}^{12}+94069263918929616324\,{x}^{13}+437576396725285446564\,{x}^{27}+3614565944605222108800\,{x}^{22}+3064515076512846852480\,{x}^{23}+{\frac{7584660010542711771792\,{x}^{25}}{5}}+37727143432895007\,{x}^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14)^2,x)

[Out]

17451466816*x+3534290697929473864098*x^20+2194577166014752240080*x^18+2945285062
308448290360*x^19+26506949038858918036881/7*x^21+2625458326972530284475/14*x^28+
2298383223254096766840*x^24+875152864622814086340*x^26+443569828128*x^2+87406679
578680*x^4+4057390785756924/5*x^5+7299544818384*x^3+16677181699666569/35*x^35+49
28210137817518464*x^31+101849676181562048256/5*x^30+67899784121041365504*x^29+11
118121133111046*x^34+126005372841925188*x^33+924039400840784712*x^32+14631040321
60519033200*x^17+872775774067455498528*x^16+197897276851452864*x^8+6077684727888
102*x^6+221699757548270194389*x^14+465517091041681015296*x^15+889942562270387136
*x^9+17344958593049772048/5*x^10+11821487501620716192*x^11+35454069480572048124*
x^12+94069263918929616324*x^13+437576396725285446564*x^27+3614565944605222108800
*x^22+3064515076512846852480*x^23+7584660010542711771792/5*x^25+3772714343289500
7*x^7

_______________________________________________________________________________________

Maxima [A]  time = 0.782346, size = 235, normalized size = 4.2 \[ \frac{16677181699666569}{35} \, x^{35} + 11118121133111046 \, x^{34} + 126005372841925188 \, x^{33} + 924039400840784712 \, x^{32} + 4928210137817518464 \, x^{31} + \frac{101849676181562048256}{5} \, x^{30} + 67899784121041365504 \, x^{29} + \frac{2625458326972530284475}{14} \, x^{28} + 437576396725285446564 \, x^{27} + 875152864622814086340 \, x^{26} + \frac{7584660010542711771792}{5} \, x^{25} + 2298383223254096766840 \, x^{24} + 3064515076512846852480 \, x^{23} + 3614565944605222108800 \, x^{22} + \frac{26506949038858918036881}{7} \, x^{21} + 3534290697929473864098 \, x^{20} + 2945285062308448290360 \, x^{19} + 2194577166014752240080 \, x^{18} + 1463104032160519033200 \, x^{17} + 872775774067455498528 \, x^{16} + 465517091041681015296 \, x^{15} + 221699757548270194389 \, x^{14} + 94069263918929616324 \, x^{13} + 35454069480572048124 \, x^{12} + 11821487501620716192 \, x^{11} + \frac{17344958593049772048}{5} \, x^{10} + 889942562270387136 \, x^{9} + 197897276851452864 \, x^{8} + 37727143432895007 \, x^{7} + 6077684727888102 \, x^{6} + \frac{4057390785756924}{5} \, x^{5} + 87406679578680 \, x^{4} + 7299544818384 \, x^{3} + 443569828128 \, x^{2} + 17451466816 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)^2*(3*x + 2)^6,x, algorithm="maxima")

[Out]

16677181699666569/35*x^35 + 11118121133111046*x^34 + 126005372841925188*x^33 + 9
24039400840784712*x^32 + 4928210137817518464*x^31 + 101849676181562048256/5*x^30
+ 67899784121041365504*x^29 + 2625458326972530284475/14*x^28 + 4375763967252854
46564*x^27 + 875152864622814086340*x^26 + 7584660010542711771792/5*x^25 + 229838
3223254096766840*x^24 + 3064515076512846852480*x^23 + 3614565944605222108800*x^2
2 + 26506949038858918036881/7*x^21 + 3534290697929473864098*x^20 + 2945285062308
448290360*x^19 + 2194577166014752240080*x^18 + 1463104032160519033200*x^17 + 872
775774067455498528*x^16 + 465517091041681015296*x^15 + 221699757548270194389*x^1
4 + 94069263918929616324*x^13 + 35454069480572048124*x^12 + 11821487501620716192
*x^11 + 17344958593049772048/5*x^10 + 889942562270387136*x^9 + 19789727685145286
4*x^8 + 37727143432895007*x^7 + 6077684727888102*x^6 + 4057390785756924/5*x^5 +
87406679578680*x^4 + 7299544818384*x^3 + 443569828128*x^2 + 17451466816*x

_______________________________________________________________________________________

Fricas [A]  time = 0.225785, size = 1, normalized size = 0.02 \[ \frac{16677181699666569}{35} x^{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac{101849676181562048256}{5} x^{30} + 67899784121041365504 x^{29} + \frac{2625458326972530284475}{14} x^{28} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac{7584660010542711771792}{5} x^{25} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac{26506949038858918036881}{7} x^{21} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac{17344958593049772048}{5} x^{10} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac{4057390785756924}{5} x^{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)^2*(3*x + 2)^6,x, algorithm="fricas")

[Out]

16677181699666569/35*x^35 + 11118121133111046*x^34 + 126005372841925188*x^33 + 9
24039400840784712*x^32 + 4928210137817518464*x^31 + 101849676181562048256/5*x^30
+ 67899784121041365504*x^29 + 2625458326972530284475/14*x^28 + 4375763967252854
46564*x^27 + 875152864622814086340*x^26 + 7584660010542711771792/5*x^25 + 229838
3223254096766840*x^24 + 3064515076512846852480*x^23 + 3614565944605222108800*x^2
2 + 26506949038858918036881/7*x^21 + 3534290697929473864098*x^20 + 2945285062308
448290360*x^19 + 2194577166014752240080*x^18 + 1463104032160519033200*x^17 + 872
775774067455498528*x^16 + 465517091041681015296*x^15 + 221699757548270194389*x^1
4 + 94069263918929616324*x^13 + 35454069480572048124*x^12 + 11821487501620716192
*x^11 + 17344958593049772048/5*x^10 + 889942562270387136*x^9 + 19789727685145286
4*x^8 + 37727143432895007*x^7 + 6077684727888102*x^6 + 4057390785756924/5*x^5 +
87406679578680*x^4 + 7299544818384*x^3 + 443569828128*x^2 + 17451466816*x

_______________________________________________________________________________________

Sympy [A]  time = 0.307388, 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.

[In]  integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14)**2,x)

[Out]

16677181699666569*x**35/35 + 11118121133111046*x**34 + 126005372841925188*x**33
+ 924039400840784712*x**32 + 4928210137817518464*x**31 + 101849676181562048256*x
**30/5 + 67899784121041365504*x**29 + 2625458326972530284475*x**28/14 + 43757639
6725285446564*x**27 + 875152864622814086340*x**26 + 7584660010542711771792*x**25
/5 + 2298383223254096766840*x**24 + 3064515076512846852480*x**23 + 3614565944605
222108800*x**22 + 26506949038858918036881*x**21/7 + 3534290697929473864098*x**20
+ 2945285062308448290360*x**19 + 2194577166014752240080*x**18 + 146310403216051
9033200*x**17 + 872775774067455498528*x**16 + 465517091041681015296*x**15 + 2216
99757548270194389*x**14 + 94069263918929616324*x**13 + 35454069480572048124*x**1
2 + 11821487501620716192*x**11 + 17344958593049772048*x**10/5 + 8899425622703871
36*x**9 + 197897276851452864*x**8 + 37727143432895007*x**7 + 6077684727888102*x*
*6 + 4057390785756924*x**5/5 + 87406679578680*x**4 + 7299544818384*x**3 + 443569
828128*x**2 + 17451466816*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.269389, size = 62, normalized size = 1.11 \[ \frac{1}{105} \,{\left (3 \, x + 2\right )}^{35} + \frac{1}{42} \,{\left (3 \, x + 2\right )}^{28} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{21} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{14} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((3*x + 2)^14 + (3*x + 2)^7 + 1)^2*(3*x + 2)^6,x, algorithm="giac")

[Out]

1/105*(3*x + 2)^35 + 1/42*(3*x + 2)^28 + 1/21*(3*x + 2)^21 + 1/21*(3*x + 2)^14 +
1/21*(3*x + 2)^7