Optimal. Leaf size=33 \[ \frac{49}{10} x^{10} (x+1)^{10}-36 x^7 (x+1)^7+81 x^4 (x+1)^4 \]
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Rubi [B] time = 0.197782, 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, Rules used = {1593, 1612} \[ \frac{49 x^{20}}{10}+49 x^{19}+\frac{441 x^{18}}{2}+588 x^{17}+1029 x^{16}+\frac{6174 x^{15}}{5}+993 x^{14}+336 x^{13}-\frac{1071 x^{12}}{2}-1211 x^{11}-\frac{12551 x^{10}}{10}-756 x^9-171 x^8+288 x^7+486 x^6+324 x^5+81 x^4 \]
Antiderivative was successfully verified.
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Rule 1593
Rule 1612
Rubi steps
\begin{align*} \int (1+2 x) \left (x+x^2\right )^3 \left (-18+7 \left (x+x^2\right )^3\right )^2 \, dx &=\int x^3 (1+x)^3 (1+2 x) \left (-18+7 \left (x+x^2\right )^3\right )^2 \, dx\\ &=\int \left (324 x^3+1620 x^4+2916 x^5+2016 x^6-1368 x^7-6804 x^8-12551 x^9-13321 x^{10}-6426 x^{11}+4368 x^{12}+13902 x^{13}+18522 x^{14}+16464 x^{15}+9996 x^{16}+3969 x^{17}+931 x^{18}+98 x^{19}\right ) \, dx\\ &=81 x^4+324 x^5+486 x^6+288 x^7-171 x^8-756 x^9-\frac{12551 x^{10}}{10}-1211 x^{11}-\frac{1071 x^{12}}{2}+336 x^{13}+993 x^{14}+\frac{6174 x^{15}}{5}+1029 x^{16}+588 x^{17}+\frac{441 x^{18}}{2}+49 x^{19}+\frac{49 x^{20}}{10}\\ \end{align*}
Mathematica [B] time = 0.006101, 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.
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Maple [B] time = 0.002, size = 87, normalized size = 2.6 \begin{align*}{\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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.992962, size = 116, normalized size = 3.52 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.1462, size = 263, normalized size = 7.97 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.07515, size = 94, normalized size = 2.85 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.22729, size = 116, normalized size = 3.52 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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