Optimal. Leaf size=95 \[ \frac {a^7 x^9}{9}+\frac {7}{10} a^6 b x^{10}+\frac {21}{11} a^5 b^2 x^{11}+\frac {35}{12} a^4 b^3 x^{12}+\frac {35}{13} a^3 b^4 x^{13}+\frac {3}{2} a^2 b^5 x^{14}+\frac {7}{15} a b^6 x^{15}+\frac {b^7 x^{16}}{16} \]
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Rubi [A] time = 0.05, antiderivative size = 95, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} \frac {3}{2} a^2 b^5 x^{14}+\frac {35}{13} a^3 b^4 x^{13}+\frac {35}{12} a^4 b^3 x^{12}+\frac {21}{11} a^5 b^2 x^{11}+\frac {7}{10} a^6 b x^{10}+\frac {a^7 x^9}{9}+\frac {7}{15} a b^6 x^{15}+\frac {b^7 x^{16}}{16} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^8 (a+b x)^7 \, dx &=\int \left (a^7 x^8+7 a^6 b x^9+21 a^5 b^2 x^{10}+35 a^4 b^3 x^{11}+35 a^3 b^4 x^{12}+21 a^2 b^5 x^{13}+7 a b^6 x^{14}+b^7 x^{15}\right ) \, dx\\ &=\frac {a^7 x^9}{9}+\frac {7}{10} a^6 b x^{10}+\frac {21}{11} a^5 b^2 x^{11}+\frac {35}{12} a^4 b^3 x^{12}+\frac {35}{13} a^3 b^4 x^{13}+\frac {3}{2} a^2 b^5 x^{14}+\frac {7}{15} a b^6 x^{15}+\frac {b^7 x^{16}}{16}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 95, normalized size = 1.00 \begin {gather*} \frac {a^7 x^9}{9}+\frac {7}{10} a^6 b x^{10}+\frac {21}{11} a^5 b^2 x^{11}+\frac {35}{12} a^4 b^3 x^{12}+\frac {35}{13} a^3 b^4 x^{13}+\frac {3}{2} a^2 b^5 x^{14}+\frac {7}{15} a b^6 x^{15}+\frac {b^7 x^{16}}{16} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^8 (a+b x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.29, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{16} x^{16} b^{7} + \frac {7}{15} x^{15} b^{6} a + \frac {3}{2} x^{14} b^{5} a^{2} + \frac {35}{13} x^{13} b^{4} a^{3} + \frac {35}{12} x^{12} b^{3} a^{4} + \frac {21}{11} x^{11} b^{2} a^{5} + \frac {7}{10} x^{10} b a^{6} + \frac {1}{9} x^{9} a^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{16} \, b^{7} x^{16} + \frac {7}{15} \, a b^{6} x^{15} + \frac {3}{2} \, a^{2} b^{5} x^{14} + \frac {35}{13} \, a^{3} b^{4} x^{13} + \frac {35}{12} \, a^{4} b^{3} x^{12} + \frac {21}{11} \, a^{5} b^{2} x^{11} + \frac {7}{10} \, a^{6} b x^{10} + \frac {1}{9} \, a^{7} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 80, normalized size = 0.84 \begin {gather*} \frac {1}{16} b^{7} x^{16}+\frac {7}{15} a \,b^{6} x^{15}+\frac {3}{2} a^{2} b^{5} x^{14}+\frac {35}{13} a^{3} b^{4} x^{13}+\frac {35}{12} a^{4} b^{3} x^{12}+\frac {21}{11} a^{5} b^{2} x^{11}+\frac {7}{10} a^{6} b \,x^{10}+\frac {1}{9} a^{7} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.40, size = 79, normalized size = 0.83 \begin {gather*} \frac {1}{16} \, b^{7} x^{16} + \frac {7}{15} \, a b^{6} x^{15} + \frac {3}{2} \, a^{2} b^{5} x^{14} + \frac {35}{13} \, a^{3} b^{4} x^{13} + \frac {35}{12} \, a^{4} b^{3} x^{12} + \frac {21}{11} \, a^{5} b^{2} x^{11} + \frac {7}{10} \, a^{6} b x^{10} + \frac {1}{9} \, a^{7} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 79, normalized size = 0.83 \begin {gather*} \frac {a^7\,x^9}{9}+\frac {7\,a^6\,b\,x^{10}}{10}+\frac {21\,a^5\,b^2\,x^{11}}{11}+\frac {35\,a^4\,b^3\,x^{12}}{12}+\frac {35\,a^3\,b^4\,x^{13}}{13}+\frac {3\,a^2\,b^5\,x^{14}}{2}+\frac {7\,a\,b^6\,x^{15}}{15}+\frac {b^7\,x^{16}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 94, normalized size = 0.99 \begin {gather*} \frac {a^{7} x^{9}}{9} + \frac {7 a^{6} b x^{10}}{10} + \frac {21 a^{5} b^{2} x^{11}}{11} + \frac {35 a^{4} b^{3} x^{12}}{12} + \frac {35 a^{3} b^{4} x^{13}}{13} + \frac {3 a^{2} b^{5} x^{14}}{2} + \frac {7 a b^{6} x^{15}}{15} + \frac {b^{7} x^{16}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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