Optimal. Leaf size=108 \[ \frac {a^8 x^4}{4}+\frac {8}{7} a^7 b x^7+\frac {14}{5} a^6 b^2 x^{10}+\frac {56}{13} a^5 b^3 x^{13}+\frac {35}{8} a^4 b^4 x^{16}+\frac {56}{19} a^3 b^5 x^{19}+\frac {14}{11} a^2 b^6 x^{22}+\frac {8}{25} a b^7 x^{25}+\frac {b^8 x^{28}}{28} \]
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Rubi [A]
time = 0.03, antiderivative size = 108, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} \frac {a^8 x^4}{4}+\frac {8}{7} a^7 b x^7+\frac {14}{5} a^6 b^2 x^{10}+\frac {56}{13} a^5 b^3 x^{13}+\frac {35}{8} a^4 b^4 x^{16}+\frac {56}{19} a^3 b^5 x^{19}+\frac {14}{11} a^2 b^6 x^{22}+\frac {8}{25} a b^7 x^{25}+\frac {b^8 x^{28}}{28} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x^3 \left (a+b x^3\right )^8 \, dx &=\int \left (a^8 x^3+8 a^7 b x^6+28 a^6 b^2 x^9+56 a^5 b^3 x^{12}+70 a^4 b^4 x^{15}+56 a^3 b^5 x^{18}+28 a^2 b^6 x^{21}+8 a b^7 x^{24}+b^8 x^{27}\right ) \, dx\\ &=\frac {a^8 x^4}{4}+\frac {8}{7} a^7 b x^7+\frac {14}{5} a^6 b^2 x^{10}+\frac {56}{13} a^5 b^3 x^{13}+\frac {35}{8} a^4 b^4 x^{16}+\frac {56}{19} a^3 b^5 x^{19}+\frac {14}{11} a^2 b^6 x^{22}+\frac {8}{25} a b^7 x^{25}+\frac {b^8 x^{28}}{28}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 108, normalized size = 1.00 \begin {gather*} \frac {a^8 x^4}{4}+\frac {8}{7} a^7 b x^7+\frac {14}{5} a^6 b^2 x^{10}+\frac {56}{13} a^5 b^3 x^{13}+\frac {35}{8} a^4 b^4 x^{16}+\frac {56}{19} a^3 b^5 x^{19}+\frac {14}{11} a^2 b^6 x^{22}+\frac {8}{25} a b^7 x^{25}+\frac {b^8 x^{28}}{28} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 91, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{4} a^{8} x^{4}+\frac {8}{7} a^{7} b \,x^{7}+\frac {14}{5} a^{6} b^{2} x^{10}+\frac {56}{13} a^{5} b^{3} x^{13}+\frac {35}{8} a^{4} b^{4} x^{16}+\frac {56}{19} a^{3} b^{5} x^{19}+\frac {14}{11} a^{2} b^{6} x^{22}+\frac {8}{25} a \,b^{7} x^{25}+\frac {1}{28} b^{8} x^{28}\) | \(91\) |
default | \(\frac {1}{4} a^{8} x^{4}+\frac {8}{7} a^{7} b \,x^{7}+\frac {14}{5} a^{6} b^{2} x^{10}+\frac {56}{13} a^{5} b^{3} x^{13}+\frac {35}{8} a^{4} b^{4} x^{16}+\frac {56}{19} a^{3} b^{5} x^{19}+\frac {14}{11} a^{2} b^{6} x^{22}+\frac {8}{25} a \,b^{7} x^{25}+\frac {1}{28} b^{8} x^{28}\) | \(91\) |
norman | \(\frac {1}{4} a^{8} x^{4}+\frac {8}{7} a^{7} b \,x^{7}+\frac {14}{5} a^{6} b^{2} x^{10}+\frac {56}{13} a^{5} b^{3} x^{13}+\frac {35}{8} a^{4} b^{4} x^{16}+\frac {56}{19} a^{3} b^{5} x^{19}+\frac {14}{11} a^{2} b^{6} x^{22}+\frac {8}{25} a \,b^{7} x^{25}+\frac {1}{28} b^{8} x^{28}\) | \(91\) |
risch | \(\frac {1}{4} a^{8} x^{4}+\frac {8}{7} a^{7} b \,x^{7}+\frac {14}{5} a^{6} b^{2} x^{10}+\frac {56}{13} a^{5} b^{3} x^{13}+\frac {35}{8} a^{4} b^{4} x^{16}+\frac {56}{19} a^{3} b^{5} x^{19}+\frac {14}{11} a^{2} b^{6} x^{22}+\frac {8}{25} a \,b^{7} x^{25}+\frac {1}{28} b^{8} x^{28}\) | \(91\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 90, normalized size = 0.83 \begin {gather*} \frac {1}{28} \, b^{8} x^{28} + \frac {8}{25} \, a b^{7} x^{25} + \frac {14}{11} \, a^{2} b^{6} x^{22} + \frac {56}{19} \, a^{3} b^{5} x^{19} + \frac {35}{8} \, a^{4} b^{4} x^{16} + \frac {56}{13} \, a^{5} b^{3} x^{13} + \frac {14}{5} \, a^{6} b^{2} x^{10} + \frac {8}{7} \, a^{7} b x^{7} + \frac {1}{4} \, a^{8} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 90, normalized size = 0.83 \begin {gather*} \frac {1}{28} \, b^{8} x^{28} + \frac {8}{25} \, a b^{7} x^{25} + \frac {14}{11} \, a^{2} b^{6} x^{22} + \frac {56}{19} \, a^{3} b^{5} x^{19} + \frac {35}{8} \, a^{4} b^{4} x^{16} + \frac {56}{13} \, a^{5} b^{3} x^{13} + \frac {14}{5} \, a^{6} b^{2} x^{10} + \frac {8}{7} \, a^{7} b x^{7} + \frac {1}{4} \, a^{8} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 107, normalized size = 0.99 \begin {gather*} \frac {a^{8} x^{4}}{4} + \frac {8 a^{7} b x^{7}}{7} + \frac {14 a^{6} b^{2} x^{10}}{5} + \frac {56 a^{5} b^{3} x^{13}}{13} + \frac {35 a^{4} b^{4} x^{16}}{8} + \frac {56 a^{3} b^{5} x^{19}}{19} + \frac {14 a^{2} b^{6} x^{22}}{11} + \frac {8 a b^{7} x^{25}}{25} + \frac {b^{8} x^{28}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.08, size = 90, normalized size = 0.83 \begin {gather*} \frac {1}{28} \, b^{8} x^{28} + \frac {8}{25} \, a b^{7} x^{25} + \frac {14}{11} \, a^{2} b^{6} x^{22} + \frac {56}{19} \, a^{3} b^{5} x^{19} + \frac {35}{8} \, a^{4} b^{4} x^{16} + \frac {56}{13} \, a^{5} b^{3} x^{13} + \frac {14}{5} \, a^{6} b^{2} x^{10} + \frac {8}{7} \, a^{7} b x^{7} + \frac {1}{4} \, a^{8} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 90, normalized size = 0.83 \begin {gather*} \frac {a^8\,x^4}{4}+\frac {8\,a^7\,b\,x^7}{7}+\frac {14\,a^6\,b^2\,x^{10}}{5}+\frac {56\,a^5\,b^3\,x^{13}}{13}+\frac {35\,a^4\,b^4\,x^{16}}{8}+\frac {56\,a^3\,b^5\,x^{19}}{19}+\frac {14\,a^2\,b^6\,x^{22}}{11}+\frac {8\,a\,b^7\,x^{25}}{25}+\frac {b^8\,x^{28}}{28} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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