Optimal. Leaf size=73 \[ \frac {a x^{13}}{13}+\frac {2 a x^{10}}{5}+\frac {6 a x^7}{7}+a x^4+a x+\frac {b x^{14}}{14}+\frac {4 b x^{11}}{11}+\frac {3 b x^8}{4}+\frac {4 b x^5}{5}+\frac {b x^2}{2} \]
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Rubi [A] time = 0.05, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {771} \begin {gather*} \frac {a x^{13}}{13}+\frac {2 a x^{10}}{5}+\frac {6 a x^7}{7}+a x^4+a x+\frac {b x^{14}}{14}+\frac {4 b x^{11}}{11}+\frac {3 b x^8}{4}+\frac {4 b x^5}{5}+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (1+x)^4 (a+b x) \left (1-x+x^2\right )^4 \, dx &=\int \left (a+b x+4 a x^3+4 b x^4+6 a x^6+6 b x^7+4 a x^9+4 b x^{10}+a x^{12}+b x^{13}\right ) \, dx\\ &=a x+\frac {b x^2}{2}+a x^4+\frac {4 b x^5}{5}+\frac {6 a x^7}{7}+\frac {3 b x^8}{4}+\frac {2 a x^{10}}{5}+\frac {4 b x^{11}}{11}+\frac {a x^{13}}{13}+\frac {b x^{14}}{14}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 73, normalized size = 1.00 \begin {gather*} \frac {a x^{13}}{13}+\frac {2 a x^{10}}{5}+\frac {6 a x^7}{7}+a x^4+a x+\frac {b x^{14}}{14}+\frac {4 b x^{11}}{11}+\frac {3 b x^8}{4}+\frac {4 b x^5}{5}+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1+x)^4 (a+b x) \left (1-x+x^2\right )^4 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.35, size = 57, normalized size = 0.78 \begin {gather*} \frac {1}{14} x^{14} b + \frac {1}{13} x^{13} a + \frac {4}{11} x^{11} b + \frac {2}{5} x^{10} a + \frac {3}{4} x^{8} b + \frac {6}{7} x^{7} a + \frac {4}{5} x^{5} b + x^{4} a + \frac {1}{2} x^{2} b + x a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 57, normalized size = 0.78 \begin {gather*} \frac {1}{14} \, b x^{14} + \frac {1}{13} \, a x^{13} + \frac {4}{11} \, b x^{11} + \frac {2}{5} \, a x^{10} + \frac {3}{4} \, b x^{8} + \frac {6}{7} \, a x^{7} + \frac {4}{5} \, b x^{5} + a x^{4} + \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 58, normalized size = 0.79 \begin {gather*} \frac {1}{14} b \,x^{14}+\frac {1}{13} a \,x^{13}+\frac {4}{11} b \,x^{11}+\frac {2}{5} a \,x^{10}+\frac {3}{4} b \,x^{8}+\frac {6}{7} a \,x^{7}+\frac {4}{5} b \,x^{5}+a \,x^{4}+\frac {1}{2} b \,x^{2}+a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 57, normalized size = 0.78 \begin {gather*} \frac {1}{14} \, b x^{14} + \frac {1}{13} \, a x^{13} + \frac {4}{11} \, b x^{11} + \frac {2}{5} \, a x^{10} + \frac {3}{4} \, b x^{8} + \frac {6}{7} \, a x^{7} + \frac {4}{5} \, b x^{5} + a x^{4} + \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 57, normalized size = 0.78 \begin {gather*} \frac {b\,x^{14}}{14}+\frac {a\,x^{13}}{13}+\frac {4\,b\,x^{11}}{11}+\frac {2\,a\,x^{10}}{5}+\frac {3\,b\,x^8}{4}+\frac {6\,a\,x^7}{7}+\frac {4\,b\,x^5}{5}+a\,x^4+\frac {b\,x^2}{2}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 70, normalized size = 0.96 \begin {gather*} \frac {a x^{13}}{13} + \frac {2 a x^{10}}{5} + \frac {6 a x^{7}}{7} + a x^{4} + a x + \frac {b x^{14}}{14} + \frac {4 b x^{11}}{11} + \frac {3 b x^{8}}{4} + \frac {4 b x^{5}}{5} + \frac {b x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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