Optimal. Leaf size=30 \[ -\frac {a^2}{11 x^{11}}-\frac {a b}{4 x^8}-\frac {b^2}{5 x^5} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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^2}{11 x^{11}}-\frac {a b}{4 x^8}-\frac {b^2}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2}{x^{12}} \, dx &=\int \left (\frac {a^2}{x^{12}}+\frac {2 a b}{x^9}+\frac {b^2}{x^6}\right ) \, dx\\ &=-\frac {a^2}{11 x^{11}}-\frac {a b}{4 x^8}-\frac {b^2}{5 x^5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{11 x^{11}}-\frac {a b}{4 x^8}-\frac {b^2}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 25, normalized size = 0.83
method | result | size |
default | \(-\frac {a^{2}}{11 x^{11}}-\frac {a b}{4 x^{8}}-\frac {b^{2}}{5 x^{5}}\) | \(25\) |
norman | \(\frac {-\frac {1}{5} b^{2} x^{6}-\frac {1}{4} a b \,x^{3}-\frac {1}{11} a^{2}}{x^{11}}\) | \(26\) |
risch | \(\frac {-\frac {1}{5} b^{2} x^{6}-\frac {1}{4} a b \,x^{3}-\frac {1}{11} a^{2}}{x^{11}}\) | \(26\) |
gosper | \(-\frac {44 b^{2} x^{6}+55 a b \,x^{3}+20 a^{2}}{220 x^{11}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 0.87 \begin {gather*} -\frac {44 \, b^{2} x^{6} + 55 \, a b x^{3} + 20 \, a^{2}}{220 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 26, normalized size = 0.87 \begin {gather*} -\frac {44 \, b^{2} x^{6} + 55 \, a b x^{3} + 20 \, a^{2}}{220 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 27, normalized size = 0.90 \begin {gather*} \frac {- 20 a^{2} - 55 a b x^{3} - 44 b^{2} x^{6}}{220 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.84, size = 26, normalized size = 0.87 \begin {gather*} -\frac {44 \, b^{2} x^{6} + 55 \, a b x^{3} + 20 \, a^{2}}{220 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 26, normalized size = 0.87 \begin {gather*} -\frac {\frac {a^2}{11}+\frac {a\,b\,x^3}{4}+\frac {b^2\,x^6}{5}}{x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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