Optimal. Leaf size=112 \[ \frac {a^6 (a+b x)^{11}}{11 b^7}-\frac {a^5 (a+b x)^{12}}{2 b^7}+\frac {15 a^4 (a+b x)^{13}}{13 b^7}-\frac {10 a^3 (a+b x)^{14}}{7 b^7}+\frac {a^2 (a+b x)^{15}}{b^7}+\frac {(a+b x)^{17}}{17 b^7}-\frac {3 a (a+b x)^{16}}{8 b^7} \]
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Rubi [A] time = 0.05, antiderivative size = 112, 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 {a^2 (a+b x)^{15}}{b^7}-\frac {10 a^3 (a+b x)^{14}}{7 b^7}+\frac {15 a^4 (a+b x)^{13}}{13 b^7}-\frac {a^5 (a+b x)^{12}}{2 b^7}+\frac {a^6 (a+b x)^{11}}{11 b^7}+\frac {(a+b x)^{17}}{17 b^7}-\frac {3 a (a+b x)^{16}}{8 b^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^6 (a+b x)^{10} \, dx &=\int \left (\frac {a^6 (a+b x)^{10}}{b^6}-\frac {6 a^5 (a+b x)^{11}}{b^6}+\frac {15 a^4 (a+b x)^{12}}{b^6}-\frac {20 a^3 (a+b x)^{13}}{b^6}+\frac {15 a^2 (a+b x)^{14}}{b^6}-\frac {6 a (a+b x)^{15}}{b^6}+\frac {(a+b x)^{16}}{b^6}\right ) \, dx\\ &=\frac {a^6 (a+b x)^{11}}{11 b^7}-\frac {a^5 (a+b x)^{12}}{2 b^7}+\frac {15 a^4 (a+b x)^{13}}{13 b^7}-\frac {10 a^3 (a+b x)^{14}}{7 b^7}+\frac {a^2 (a+b x)^{15}}{b^7}-\frac {3 a (a+b x)^{16}}{8 b^7}+\frac {(a+b x)^{17}}{17 b^7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 126, normalized size = 1.12 \begin {gather*} \frac {a^{10} x^7}{7}+\frac {5}{4} a^9 b x^8+5 a^8 b^2 x^9+12 a^7 b^3 x^{10}+\frac {210}{11} a^6 b^4 x^{11}+21 a^5 b^5 x^{12}+\frac {210}{13} a^4 b^6 x^{13}+\frac {60}{7} a^3 b^7 x^{14}+3 a^2 b^8 x^{15}+\frac {5}{8} a b^9 x^{16}+\frac {b^{10} x^{17}}{17} \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)^{10} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.97, size = 112, normalized size = 1.00 \begin {gather*} \frac {1}{17} x^{17} b^{10} + \frac {5}{8} x^{16} b^{9} a + 3 x^{15} b^{8} a^{2} + \frac {60}{7} x^{14} b^{7} a^{3} + \frac {210}{13} x^{13} b^{6} a^{4} + 21 x^{12} b^{5} a^{5} + \frac {210}{11} x^{11} b^{4} a^{6} + 12 x^{10} b^{3} a^{7} + 5 x^{9} b^{2} a^{8} + \frac {5}{4} x^{8} b a^{9} + \frac {1}{7} x^{7} a^{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 112, normalized size = 1.00 \begin {gather*} \frac {1}{17} \, b^{10} x^{17} + \frac {5}{8} \, a b^{9} x^{16} + 3 \, a^{2} b^{8} x^{15} + \frac {60}{7} \, a^{3} b^{7} x^{14} + \frac {210}{13} \, a^{4} b^{6} x^{13} + 21 \, a^{5} b^{5} x^{12} + \frac {210}{11} \, a^{6} b^{4} x^{11} + 12 \, a^{7} b^{3} x^{10} + 5 \, a^{8} b^{2} x^{9} + \frac {5}{4} \, a^{9} b x^{8} + \frac {1}{7} \, a^{10} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 113, normalized size = 1.01 \begin {gather*} \frac {1}{17} b^{10} x^{17}+\frac {5}{8} a \,b^{9} x^{16}+3 a^{2} b^{8} x^{15}+\frac {60}{7} a^{3} b^{7} x^{14}+\frac {210}{13} a^{4} b^{6} x^{13}+21 a^{5} b^{5} x^{12}+\frac {210}{11} a^{6} b^{4} x^{11}+12 a^{7} b^{3} x^{10}+5 a^{8} b^{2} x^{9}+\frac {5}{4} a^{9} b \,x^{8}+\frac {1}{7} a^{10} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 112, normalized size = 1.00 \begin {gather*} \frac {1}{17} \, b^{10} x^{17} + \frac {5}{8} \, a b^{9} x^{16} + 3 \, a^{2} b^{8} x^{15} + \frac {60}{7} \, a^{3} b^{7} x^{14} + \frac {210}{13} \, a^{4} b^{6} x^{13} + 21 \, a^{5} b^{5} x^{12} + \frac {210}{11} \, a^{6} b^{4} x^{11} + 12 \, a^{7} b^{3} x^{10} + 5 \, a^{8} b^{2} x^{9} + \frac {5}{4} \, a^{9} b x^{8} + \frac {1}{7} \, a^{10} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 112, normalized size = 1.00 \begin {gather*} \frac {a^{10}\,x^7}{7}+\frac {5\,a^9\,b\,x^8}{4}+5\,a^8\,b^2\,x^9+12\,a^7\,b^3\,x^{10}+\frac {210\,a^6\,b^4\,x^{11}}{11}+21\,a^5\,b^5\,x^{12}+\frac {210\,a^4\,b^6\,x^{13}}{13}+\frac {60\,a^3\,b^7\,x^{14}}{7}+3\,a^2\,b^8\,x^{15}+\frac {5\,a\,b^9\,x^{16}}{8}+\frac {b^{10}\,x^{17}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 128, normalized size = 1.14 \begin {gather*} \frac {a^{10} x^{7}}{7} + \frac {5 a^{9} b x^{8}}{4} + 5 a^{8} b^{2} x^{9} + 12 a^{7} b^{3} x^{10} + \frac {210 a^{6} b^{4} x^{11}}{11} + 21 a^{5} b^{5} x^{12} + \frac {210 a^{4} b^{6} x^{13}}{13} + \frac {60 a^{3} b^{7} x^{14}}{7} + 3 a^{2} b^{8} x^{15} + \frac {5 a b^{9} x^{16}}{8} + \frac {b^{10} x^{17}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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