Optimal. Leaf size=69 \[ -\frac {a^5}{30 x^{30}}-\frac {5 a^4 b}{27 x^{27}}-\frac {5 a^3 b^2}{12 x^{24}}-\frac {10 a^2 b^3}{21 x^{21}}-\frac {5 a b^4}{18 x^{18}}-\frac {b^5}{15 x^{15}} \]
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Rubi [A]
time = 0.02, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} -\frac {a^5}{30 x^{30}}-\frac {5 a^4 b}{27 x^{27}}-\frac {5 a^3 b^2}{12 x^{24}}-\frac {10 a^2 b^3}{21 x^{21}}-\frac {5 a b^4}{18 x^{18}}-\frac {b^5}{15 x^{15}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^{31}} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^5}{x^{11}} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (\frac {a^5}{x^{11}}+\frac {5 a^4 b}{x^{10}}+\frac {10 a^3 b^2}{x^9}+\frac {10 a^2 b^3}{x^8}+\frac {5 a b^4}{x^7}+\frac {b^5}{x^6}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5}{30 x^{30}}-\frac {5 a^4 b}{27 x^{27}}-\frac {5 a^3 b^2}{12 x^{24}}-\frac {10 a^2 b^3}{21 x^{21}}-\frac {5 a b^4}{18 x^{18}}-\frac {b^5}{15 x^{15}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} -\frac {a^5}{30 x^{30}}-\frac {5 a^4 b}{27 x^{27}}-\frac {5 a^3 b^2}{12 x^{24}}-\frac {10 a^2 b^3}{21 x^{21}}-\frac {5 a b^4}{18 x^{18}}-\frac {b^5}{15 x^{15}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 58, normalized size = 0.84
method | result | size |
default | \(-\frac {a^{5}}{30 x^{30}}-\frac {5 a^{4} b}{27 x^{27}}-\frac {5 a^{3} b^{2}}{12 x^{24}}-\frac {10 a^{2} b^{3}}{21 x^{21}}-\frac {5 a \,b^{4}}{18 x^{18}}-\frac {b^{5}}{15 x^{15}}\) | \(58\) |
norman | \(\frac {-\frac {5}{18} a \,b^{4} x^{12}-\frac {1}{15} b^{5} x^{15}-\frac {5}{12} a^{3} b^{2} x^{6}-\frac {10}{21} a^{2} b^{3} x^{9}-\frac {5}{27} a^{4} b \,x^{3}-\frac {1}{30} a^{5}}{x^{30}}\) | \(59\) |
risch | \(\frac {-\frac {5}{18} a \,b^{4} x^{12}-\frac {1}{15} b^{5} x^{15}-\frac {5}{12} a^{3} b^{2} x^{6}-\frac {10}{21} a^{2} b^{3} x^{9}-\frac {5}{27} a^{4} b \,x^{3}-\frac {1}{30} a^{5}}{x^{30}}\) | \(59\) |
gosper | \(-\frac {252 b^{5} x^{15}+1050 a \,b^{4} x^{12}+1800 a^{2} b^{3} x^{9}+1575 a^{3} b^{2} x^{6}+700 a^{4} b \,x^{3}+126 a^{5}}{3780 x^{30}}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 59, normalized size = 0.86 \begin {gather*} -\frac {252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 59, normalized size = 0.86 \begin {gather*} -\frac {252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.34, size = 63, normalized size = 0.91 \begin {gather*} \frac {- 126 a^{5} - 700 a^{4} b x^{3} - 1575 a^{3} b^{2} x^{6} - 1800 a^{2} b^{3} x^{9} - 1050 a b^{4} x^{12} - 252 b^{5} x^{15}}{3780 x^{30}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.85, size = 59, normalized size = 0.86 \begin {gather*} -\frac {252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 59, normalized size = 0.86 \begin {gather*} -\frac {\frac {a^5}{30}+\frac {5\,a^4\,b\,x^3}{27}+\frac {5\,a^3\,b^2\,x^6}{12}+\frac {10\,a^2\,b^3\,x^9}{21}+\frac {5\,a\,b^4\,x^{12}}{18}+\frac {b^5\,x^{15}}{15}}{x^{30}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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