Optimal. Leaf size=61 \[ -\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \]
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Rubi [A]
time = 0.02, antiderivative size = 61, 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^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^9} \, dx &=\int \left (10 a^2 b^3+\frac {a^5}{x^9}+\frac {5 a^4 b}{x^6}+\frac {10 a^3 b^2}{x^3}+5 a b^4 x^3+b^5 x^6\right ) \, dx\\ &=-\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 61, normalized size = 1.00 \begin {gather*} -\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 56, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{5}}{8 x^{8}}-\frac {a^{4} b}{x^{5}}-\frac {5 a^{3} b^{2}}{x^{2}}+10 a^{2} b^{3} x +\frac {5 a \,b^{4} x^{4}}{4}+\frac {b^{5} x^{7}}{7}\) | \(56\) |
risch | \(\frac {b^{5} x^{7}}{7}+\frac {5 a \,b^{4} x^{4}}{4}+10 a^{2} b^{3} x +\frac {-5 a^{3} b^{2} x^{6}-a^{4} b \,x^{3}-\frac {1}{8} a^{5}}{x^{8}}\) | \(58\) |
norman | \(\frac {-\frac {1}{8} a^{5}-a^{4} b \,x^{3}-5 a^{3} b^{2} x^{6}+10 a^{2} b^{3} x^{9}+\frac {5}{4} a \,b^{4} x^{12}+\frac {1}{7} b^{5} x^{15}}{x^{8}}\) | \(59\) |
gosper | \(-\frac {-8 b^{5} x^{15}-70 a \,b^{4} x^{12}-560 a^{2} b^{3} x^{9}+280 a^{3} b^{2} x^{6}+56 a^{4} b \,x^{3}+7 a^{5}}{56 x^{8}}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 56, normalized size = 0.92 \begin {gather*} \frac {1}{7} \, b^{5} x^{7} + \frac {5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac {40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 59, normalized size = 0.97 \begin {gather*} \frac {8 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 560 \, a^{2} b^{3} x^{9} - 280 \, a^{3} b^{2} x^{6} - 56 \, a^{4} b x^{3} - 7 \, a^{5}}{56 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 61, normalized size = 1.00 \begin {gather*} 10 a^{2} b^{3} x + \frac {5 a b^{4} x^{4}}{4} + \frac {b^{5} x^{7}}{7} + \frac {- a^{5} - 8 a^{4} b x^{3} - 40 a^{3} b^{2} x^{6}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.82, size = 56, normalized size = 0.92 \begin {gather*} \frac {1}{7} \, b^{5} x^{7} + \frac {5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac {40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 57, normalized size = 0.93 \begin {gather*} \frac {b^5\,x^7}{7}-\frac {\frac {a^5}{8}+a^4\,b\,x^3+5\,a^3\,b^2\,x^6}{x^8}+10\,a^2\,b^3\,x+\frac {5\,a\,b^4\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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