3.221 \(\int (1+2 x) \left (x+x^2\right )^3 \left (-18+7 \left (x+x^2\right )^3\right )^2 \, dx\)

Optimal. Leaf size=33 \[ \frac{49}{10} x^{10} (x+1)^{10}-36 x^7 (x+1)^7+81 x^4 (x+1)^4 \]

[Out]

81*x^4*(1 + x)^4 - 36*x^7*(1 + x)^7 + (49*x^10*(1 + x)^10)/10

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Rubi [B]  time = 0.317868, antiderivative size = 96, normalized size of antiderivative = 2.91, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{49 x^{20}}{10}+49 x^{19}+\frac{441 x^{18}}{2}+588 x^{17}+1029 x^{16}+\frac{6174 x^{15}}{5}+993 x^{14}+336 x^{13}-\frac{1071 x^{12}}{2}-1211 x^{11}-\frac{12551 x^{10}}{10}-756 x^9-171 x^8+288 x^7+486 x^6+324 x^5+81 x^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 + 2*x)*(x + x^2)^3*(-18 + 7*(x + x^2)^3)^2,x]

[Out]

81*x^4 + 324*x^5 + 486*x^6 + 288*x^7 - 171*x^8 - 756*x^9 - (12551*x^10)/10 - 121
1*x^11 - (1071*x^12)/2 + 336*x^13 + 993*x^14 + (6174*x^15)/5 + 1029*x^16 + 588*x
^17 + (441*x^18)/2 + 49*x^19 + (49*x^20)/10

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Rubi in Sympy [A]  time = 27.5124, size = 94, normalized size = 2.85 \[ \frac{49 x^{20}}{10} + 49 x^{19} + \frac{441 x^{18}}{2} + 588 x^{17} + 1029 x^{16} + \frac{6174 x^{15}}{5} + 993 x^{14} + 336 x^{13} - \frac{1071 x^{12}}{2} - 1211 x^{11} - \frac{12551 x^{10}}{10} - 756 x^{9} - 171 x^{8} + 288 x^{7} + 486 x^{6} + 324 x^{5} + 81 x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1+2*x)*(x**2+x)**3*(-18+7*(x**2+x)**3)**2,x)

[Out]

49*x**20/10 + 49*x**19 + 441*x**18/2 + 588*x**17 + 1029*x**16 + 6174*x**15/5 + 9
93*x**14 + 336*x**13 - 1071*x**12/2 - 1211*x**11 - 12551*x**10/10 - 756*x**9 - 1
71*x**8 + 288*x**7 + 486*x**6 + 324*x**5 + 81*x**4

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Mathematica [B]  time = 0.00910928, size = 96, normalized size = 2.91 \[ \frac{49 x^{20}}{10}+49 x^{19}+\frac{441 x^{18}}{2}+588 x^{17}+1029 x^{16}+\frac{6174 x^{15}}{5}+993 x^{14}+336 x^{13}-\frac{1071 x^{12}}{2}-1211 x^{11}-\frac{12551 x^{10}}{10}-756 x^9-171 x^8+288 x^7+486 x^6+324 x^5+81 x^4 \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + 2*x)*(x + x^2)^3*(-18 + 7*(x + x^2)^3)^2,x]

[Out]

81*x^4 + 324*x^5 + 486*x^6 + 288*x^7 - 171*x^8 - 756*x^9 - (12551*x^10)/10 - 121
1*x^11 - (1071*x^12)/2 + 336*x^13 + 993*x^14 + (6174*x^15)/5 + 1029*x^16 + 588*x
^17 + (441*x^18)/2 + 49*x^19 + (49*x^20)/10

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Maple [B]  time = 0.002, size = 87, normalized size = 2.6 \[{\frac{49\,{x}^{20}}{10}}+49\,{x}^{19}+{\frac{441\,{x}^{18}}{2}}+588\,{x}^{17}+1029\,{x}^{16}+{\frac{6174\,{x}^{15}}{5}}+993\,{x}^{14}+336\,{x}^{13}-{\frac{1071\,{x}^{12}}{2}}-1211\,{x}^{11}-{\frac{12551\,{x}^{10}}{10}}-756\,{x}^{9}-171\,{x}^{8}+288\,{x}^{7}+486\,{x}^{6}+324\,{x}^{5}+81\,{x}^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+2*x)*(x^2+x)^3*(-18+7*(x^2+x)^3)^2,x)

[Out]

49/10*x^20+49*x^19+441/2*x^18+588*x^17+1029*x^16+6174/5*x^15+993*x^14+336*x^13-1
071/2*x^12-1211*x^11-12551/10*x^10-756*x^9-171*x^8+288*x^7+486*x^6+324*x^5+81*x^
4

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Maxima [A]  time = 0.830847, size = 116, normalized size = 3.52 \[ \frac{49}{10} \, x^{20} + 49 \, x^{19} + \frac{441}{2} \, x^{18} + 588 \, x^{17} + 1029 \, x^{16} + \frac{6174}{5} \, x^{15} + 993 \, x^{14} + 336 \, x^{13} - \frac{1071}{2} \, x^{12} - 1211 \, x^{11} - \frac{12551}{10} \, x^{10} - 756 \, x^{9} - 171 \, x^{8} + 288 \, x^{7} + 486 \, x^{6} + 324 \, x^{5} + 81 \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((7*(x^2 + x)^3 - 18)^2*(x^2 + x)^3*(2*x + 1),x, algorithm="maxima")

[Out]

49/10*x^20 + 49*x^19 + 441/2*x^18 + 588*x^17 + 1029*x^16 + 6174/5*x^15 + 993*x^1
4 + 336*x^13 - 1071/2*x^12 - 1211*x^11 - 12551/10*x^10 - 756*x^9 - 171*x^8 + 288
*x^7 + 486*x^6 + 324*x^5 + 81*x^4

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Fricas [A]  time = 0.232719, size = 1, normalized size = 0.03 \[ \frac{49}{10} x^{20} + 49 x^{19} + \frac{441}{2} x^{18} + 588 x^{17} + 1029 x^{16} + \frac{6174}{5} x^{15} + 993 x^{14} + 336 x^{13} - \frac{1071}{2} x^{12} - 1211 x^{11} - \frac{12551}{10} x^{10} - 756 x^{9} - 171 x^{8} + 288 x^{7} + 486 x^{6} + 324 x^{5} + 81 x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((7*(x^2 + x)^3 - 18)^2*(x^2 + x)^3*(2*x + 1),x, algorithm="fricas")

[Out]

49/10*x^20 + 49*x^19 + 441/2*x^18 + 588*x^17 + 1029*x^16 + 6174/5*x^15 + 993*x^1
4 + 336*x^13 - 1071/2*x^12 - 1211*x^11 - 12551/10*x^10 - 756*x^9 - 171*x^8 + 288
*x^7 + 486*x^6 + 324*x^5 + 81*x^4

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Sympy [A]  time = 0.132587, size = 94, normalized size = 2.85 \[ \frac{49 x^{20}}{10} + 49 x^{19} + \frac{441 x^{18}}{2} + 588 x^{17} + 1029 x^{16} + \frac{6174 x^{15}}{5} + 993 x^{14} + 336 x^{13} - \frac{1071 x^{12}}{2} - 1211 x^{11} - \frac{12551 x^{10}}{10} - 756 x^{9} - 171 x^{8} + 288 x^{7} + 486 x^{6} + 324 x^{5} + 81 x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1+2*x)*(x**2+x)**3*(-18+7*(x**2+x)**3)**2,x)

[Out]

49*x**20/10 + 49*x**19 + 441*x**18/2 + 588*x**17 + 1029*x**16 + 6174*x**15/5 + 9
93*x**14 + 336*x**13 - 1071*x**12/2 - 1211*x**11 - 12551*x**10/10 - 756*x**9 - 1
71*x**8 + 288*x**7 + 486*x**6 + 324*x**5 + 81*x**4

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GIAC/XCAS [A]  time = 0.257468, size = 116, normalized size = 3.52 \[ \frac{49}{10} \, x^{20} + 49 \, x^{19} + \frac{441}{2} \, x^{18} + 588 \, x^{17} + 1029 \, x^{16} + \frac{6174}{5} \, x^{15} + 993 \, x^{14} + 336 \, x^{13} - \frac{1071}{2} \, x^{12} - 1211 \, x^{11} - \frac{12551}{10} \, x^{10} - 756 \, x^{9} - 171 \, x^{8} + 288 \, x^{7} + 486 \, x^{6} + 324 \, x^{5} + 81 \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((7*(x^2 + x)^3 - 18)^2*(x^2 + x)^3*(2*x + 1),x, algorithm="giac")

[Out]

49/10*x^20 + 49*x^19 + 441/2*x^18 + 588*x^17 + 1029*x^16 + 6174/5*x^15 + 993*x^1
4 + 336*x^13 - 1071/2*x^12 - 1211*x^11 - 12551/10*x^10 - 756*x^9 - 171*x^8 + 288
*x^7 + 486*x^6 + 324*x^5 + 81*x^4