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]
________________________________________________________________________________________
Rubi [B] time = 0.15, antiderivative size = 96, normalized size of antiderivative = 2.91, number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {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.
[In]
[Out]
Rule 1612
Rubi steps
\begin {align*} \int x^3 (1+x)^3 (1+2 x) \left (-18+7 x^3 (1+x)^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 = 0.00, 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]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.72, size = 86, normalized size = 2.61 \[ \frac {49}{10} x^{20} + 49 x^{19} + \frac {441}{2} x^{18} + 588 x^{17} + 1029 x^{16} + \frac {6174}{5} x^{15} + 993 x^{14} + 336 x^{13} - \frac {1071}{2} x^{12} - 1211 x^{11} - \frac {12551}{10} x^{10} - 756 x^{9} - 171 x^{8} + 288 x^{7} + 486 x^{6} + 324 x^{5} + 81 x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 28, normalized size = 0.85 \[ \frac {49}{10} \, {\left (x^{2} + x\right )}^{10} - 36 \, {\left (x^{2} + x\right )}^{7} + 81 \, {\left (x^{2} + x\right )}^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 87, normalized size = 2.64 \[ \frac {49}{10} x^{20}+49 x^{19}+\frac {441}{2} x^{18}+588 x^{17}+1029 x^{16}+\frac {6174}{5} x^{15}+993 x^{14}+336 x^{13}-\frac {1071}{2} x^{12}-1211 x^{11}-\frac {12551}{10} x^{10}-756 x^{9}-171 x^{8}+288 x^{7}+486 x^{6}+324 x^{5}+81 x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.45, size = 86, normalized size = 2.61 \[ \frac {49}{10} \, x^{20} + 49 \, x^{19} + \frac {441}{2} \, x^{18} + 588 \, x^{17} + 1029 \, x^{16} + \frac {6174}{5} \, x^{15} + 993 \, x^{14} + 336 \, x^{13} - \frac {1071}{2} \, x^{12} - 1211 \, x^{11} - \frac {12551}{10} \, x^{10} - 756 \, x^{9} - 171 \, x^{8} + 288 \, x^{7} + 486 \, x^{6} + 324 \, x^{5} + 81 \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.19, size = 86, normalized size = 2.61 \[ \frac {49\,x^{20}}{10}+49\,x^{19}+\frac {441\,x^{18}}{2}+588\,x^{17}+1029\,x^{16}+\frac {6174\,x^{15}}{5}+993\,x^{14}+336\,x^{13}-\frac {1071\,x^{12}}{2}-1211\,x^{11}-\frac {12551\,x^{10}}{10}-756\,x^9-171\,x^8+288\,x^7+486\,x^6+324\,x^5+81\,x^4 \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.09, 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]
[Out]
________________________________________________________________________________________