Optimal. Leaf size=19 \[ -\frac {\left (a+b x^3\right )^3}{9 a x^9} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270}
\begin {gather*} -\frac {\left (a+b x^3\right )^3}{9 a x^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2}{x^{10}} \, dx &=-\frac {\left (a+b x^3\right )^3}{9 a x^9}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.58 \begin {gather*} -\frac {a^2}{9 x^9}-\frac {a b}{3 x^6}-\frac {b^2}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 25, normalized size = 1.32
method | result | size |
gosper | \(-\frac {3 b^{2} x^{6}+3 a b \,x^{3}+a^{2}}{9 x^{9}}\) | \(25\) |
default | \(-\frac {a^{2}}{9 x^{9}}-\frac {a b}{3 x^{6}}-\frac {b^{2}}{3 x^{3}}\) | \(25\) |
norman | \(\frac {-\frac {1}{3} b^{2} x^{6}-\frac {1}{3} a b \,x^{3}-\frac {1}{9} a^{2}}{x^{9}}\) | \(26\) |
risch | \(\frac {-\frac {1}{3} b^{2} x^{6}-\frac {1}{3} a b \,x^{3}-\frac {1}{9} a^{2}}{x^{9}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 26, normalized size = 1.37 \begin {gather*} \frac {- a^{2} - 3 a b x^{3} - 3 b^{2} x^{6}}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.15, size = 24, normalized size = 1.26 \begin {gather*} -\frac {3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 26, normalized size = 1.37 \begin {gather*} -\frac {\frac {a^2}{9}+\frac {a\,b\,x^3}{3}+\frac {b^2\,x^6}{3}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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