Optimal. Leaf size=66 \[ \frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \]
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Rubi [A] time = 0.03, antiderivative size = 66, 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*} a^2 b^3 x^{10}+\frac {10}{9} a^3 b^2 x^9+\frac {5}{8} a^4 b x^8+\frac {a^5 x^7}{7}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^6 (a+b x)^5 \, dx &=\int \left (a^5 x^6+5 a^4 b x^7+10 a^3 b^2 x^8+10 a^2 b^3 x^9+5 a b^4 x^{10}+b^5 x^{11}\right ) \, dx\\ &=\frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 66, normalized size = 1.00 \begin {gather*} \frac {a^5 x^7}{7}+\frac {5}{8} a^4 b x^8+\frac {10}{9} a^3 b^2 x^9+a^2 b^3 x^{10}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{12}}{12} \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^6 (a+b x)^5 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.84, size = 56, normalized size = 0.85 \begin {gather*} \frac {1}{12} x^{12} b^{5} + \frac {5}{11} x^{11} b^{4} a + x^{10} b^{3} a^{2} + \frac {10}{9} x^{9} b^{2} a^{3} + \frac {5}{8} x^{8} b a^{4} + \frac {1}{7} x^{7} a^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 56, normalized size = 0.85 \begin {gather*} \frac {1}{12} \, b^{5} x^{12} + \frac {5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{8} \, a^{4} b x^{8} + \frac {1}{7} \, a^{5} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 57, normalized size = 0.86 \begin {gather*} \frac {1}{12} b^{5} x^{12}+\frac {5}{11} a \,b^{4} x^{11}+a^{2} b^{3} x^{10}+\frac {10}{9} a^{3} b^{2} x^{9}+\frac {5}{8} a^{4} b \,x^{8}+\frac {1}{7} a^{5} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 56, normalized size = 0.85 \begin {gather*} \frac {1}{12} \, b^{5} x^{12} + \frac {5}{11} \, a b^{4} x^{11} + a^{2} b^{3} x^{10} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{8} \, a^{4} b x^{8} + \frac {1}{7} \, a^{5} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 56, normalized size = 0.85 \begin {gather*} \frac {a^5\,x^7}{7}+\frac {5\,a^4\,b\,x^8}{8}+\frac {10\,a^3\,b^2\,x^9}{9}+a^2\,b^3\,x^{10}+\frac {5\,a\,b^4\,x^{11}}{11}+\frac {b^5\,x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 63, normalized size = 0.95 \begin {gather*} \frac {a^{5} x^{7}}{7} + \frac {5 a^{4} b x^{8}}{8} + \frac {10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac {5 a b^{4} x^{11}}{11} + \frac {b^{5} x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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