Optimal. Leaf size=23 \[ \frac {1}{26} \left (x^2+1\right )^{13}-\frac {1}{24} \left (x^2+1\right )^{12} \]
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Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {28, 266, 43} \[ \frac {1}{26} \left (x^2+1\right )^{13}-\frac {1}{24} \left (x^2+1\right )^{12} \]
Antiderivative was successfully verified.
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Rule 28
Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^3 \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx &=\int x^3 \left (1+x^2\right )^{11} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int x (1+x)^{11} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (-(1+x)^{11}+(1+x)^{12}\right ) \, dx,x,x^2\right )\\ &=-\frac {1}{24} \left (1+x^2\right )^{12}+\frac {1}{26} \left (1+x^2\right )^{13}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 83, normalized size = 3.61 \[ \frac {x^{26}}{26}+\frac {11 x^{24}}{24}+\frac {5 x^{22}}{2}+\frac {33 x^{20}}{4}+\frac {55 x^{18}}{3}+\frac {231 x^{16}}{8}+33 x^{14}+\frac {55 x^{12}}{2}+\frac {33 x^{10}}{2}+\frac {55 x^8}{8}+\frac {11 x^6}{6}+\frac {x^4}{4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.49, size = 61, normalized size = 2.65 \[ \frac {1}{26} x^{26} + \frac {11}{24} x^{24} + \frac {5}{2} x^{22} + \frac {33}{4} x^{20} + \frac {55}{3} x^{18} + \frac {231}{8} x^{16} + 33 x^{14} + \frac {55}{2} x^{12} + \frac {33}{2} x^{10} + \frac {55}{8} x^{8} + \frac {11}{6} x^{6} + \frac {1}{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.36, size = 61, normalized size = 2.65 \[ \frac {1}{26} \, x^{26} + \frac {11}{24} \, x^{24} + \frac {5}{2} \, x^{22} + \frac {33}{4} \, x^{20} + \frac {55}{3} \, x^{18} + \frac {231}{8} \, x^{16} + 33 \, x^{14} + \frac {55}{2} \, x^{12} + \frac {33}{2} \, x^{10} + \frac {55}{8} \, x^{8} + \frac {11}{6} \, x^{6} + \frac {1}{4} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 62, normalized size = 2.70 \[ \frac {1}{26} x^{26}+\frac {11}{24} x^{24}+\frac {5}{2} x^{22}+\frac {33}{4} x^{20}+\frac {55}{3} x^{18}+\frac {231}{8} x^{16}+33 x^{14}+\frac {55}{2} x^{12}+\frac {33}{2} x^{10}+\frac {55}{8} x^{8}+\frac {11}{6} x^{6}+\frac {1}{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.56, size = 61, normalized size = 2.65 \[ \frac {1}{26} \, x^{26} + \frac {11}{24} \, x^{24} + \frac {5}{2} \, x^{22} + \frac {33}{4} \, x^{20} + \frac {55}{3} \, x^{18} + \frac {231}{8} \, x^{16} + 33 \, x^{14} + \frac {55}{2} \, x^{12} + \frac {33}{2} \, x^{10} + \frac {55}{8} \, x^{8} + \frac {11}{6} \, x^{6} + \frac {1}{4} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 61, normalized size = 2.65 \[ \frac {x^{26}}{26}+\frac {11\,x^{24}}{24}+\frac {5\,x^{22}}{2}+\frac {33\,x^{20}}{4}+\frac {55\,x^{18}}{3}+\frac {231\,x^{16}}{8}+33\,x^{14}+\frac {55\,x^{12}}{2}+\frac {33\,x^{10}}{2}+\frac {55\,x^8}{8}+\frac {11\,x^6}{6}+\frac {x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 75, normalized size = 3.26 \[ \frac {x^{26}}{26} + \frac {11 x^{24}}{24} + \frac {5 x^{22}}{2} + \frac {33 x^{20}}{4} + \frac {55 x^{18}}{3} + \frac {231 x^{16}}{8} + 33 x^{14} + \frac {55 x^{12}}{2} + \frac {33 x^{10}}{2} + \frac {55 x^{8}}{8} + \frac {11 x^{6}}{6} + \frac {x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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