Optimal. Leaf size=30 \[ -\frac {a^2}{10 x^{10}}-\frac {2 a b}{7 x^7}-\frac {b^2}{4 x^4} \]
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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}{10 x^{10}}-\frac {2 a b}{7 x^7}-\frac {b^2}{4 x^4} \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^{11}} \, dx &=\int \left (\frac {a^2}{x^{11}}+\frac {2 a b}{x^8}+\frac {b^2}{x^5}\right ) \, dx\\ &=-\frac {a^2}{10 x^{10}}-\frac {2 a b}{7 x^7}-\frac {b^2}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{10 x^{10}}-\frac {2 a b}{7 x^7}-\frac {b^2}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 25, normalized size = 0.83
method | result | size |
default | \(-\frac {a^{2}}{10 x^{10}}-\frac {2 a b}{7 x^{7}}-\frac {b^{2}}{4 x^{4}}\) | \(25\) |
norman | \(\frac {-\frac {1}{4} b^{2} x^{6}-\frac {2}{7} a b \,x^{3}-\frac {1}{10} a^{2}}{x^{10}}\) | \(26\) |
risch | \(\frac {-\frac {1}{4} b^{2} x^{6}-\frac {2}{7} a b \,x^{3}-\frac {1}{10} a^{2}}{x^{10}}\) | \(26\) |
gosper | \(-\frac {35 b^{2} x^{6}+40 a b \,x^{3}+14 a^{2}}{140 x^{10}}\) | \(27\) |
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 {35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \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 {35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \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 {- 14 a^{2} - 40 a b x^{3} - 35 b^{2} x^{6}}{140 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.69, size = 26, normalized size = 0.87 \begin {gather*} -\frac {35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 26, normalized size = 0.87 \begin {gather*} -\frac {\frac {a^2}{10}+\frac {2\,a\,b\,x^3}{7}+\frac {b^2\,x^6}{4}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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