Optimal. Leaf size=37 \[ -\frac {a^3}{9 x^9}-\frac {a^2 b}{2 x^6}-\frac {a b^2}{x^3}+b^3 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 37, 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^3}{9 x^9}-\frac {a^2 b}{2 x^6}-\frac {a b^2}{x^3}+b^3 \log (x) \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 )^3}{x^{10}} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^3}{x^4} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (\frac {a^3}{x^4}+\frac {3 a^2 b}{x^3}+\frac {3 a b^2}{x^2}+\frac {b^3}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^3}{9 x^9}-\frac {a^2 b}{2 x^6}-\frac {a b^2}{x^3}+b^3 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} -\frac {a^3}{9 x^9}-\frac {a^2 b}{2 x^6}-\frac {a b^2}{x^3}+b^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 34, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{3}}{9 x^{9}}-\frac {a^{2} b}{2 x^{6}}-\frac {a \,b^{2}}{x^{3}}+b^{3} \ln \left (x \right )\) | \(34\) |
norman | \(\frac {-\frac {1}{9} a^{3}-a \,b^{2} x^{6}-\frac {1}{2} a^{2} b \,x^{3}}{x^{9}}+b^{3} \ln \left (x \right )\) | \(36\) |
risch | \(\frac {-\frac {1}{9} a^{3}-a \,b^{2} x^{6}-\frac {1}{2} a^{2} b \,x^{3}}{x^{9}}+b^{3} \ln \left (x \right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 39, normalized size = 1.05 \begin {gather*} \frac {1}{3} \, b^{3} \log \left (x^{3}\right ) - \frac {18 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3}}{18 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 39, normalized size = 1.05 \begin {gather*} \frac {18 \, b^{3} x^{9} \log \left (x\right ) - 18 \, a b^{2} x^{6} - 9 \, a^{2} b x^{3} - 2 \, a^{3}}{18 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 37, normalized size = 1.00 \begin {gather*} b^{3} \log {\left (x \right )} + \frac {- 2 a^{3} - 9 a^{2} b x^{3} - 18 a b^{2} x^{6}}{18 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.61, size = 45, normalized size = 1.22 \begin {gather*} b^{3} \log \left ({\left | x \right |}\right ) - \frac {11 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3}}{18 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 35, normalized size = 0.95 \begin {gather*} b^3\,\ln \left (x\right )-\frac {\frac {a^3}{9}+\frac {a^2\,b\,x^3}{2}+a\,b^2\,x^6}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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