Optimal. Leaf size=16 \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
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Rubi [A] time = 0.0053067, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {28, 261} \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a^2+2 a b x^2+b^2 x^4\right )^3} \, dx &=b^6 \int \frac{x}{\left (a b+b^2 x^2\right )^6} \, dx\\ &=-\frac{1}{10 b \left (a+b x^2\right )^5}\\ \end{align*}
Mathematica [A] time = 0.0028531, size = 16, normalized size = 1. \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.047, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{10\,b \left ( b{x}^{2}+a \right ) ^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.08085, size = 80, normalized size = 5. \begin{align*} -\frac{1}{10 \,{\left (b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.68132, size = 122, normalized size = 7.62 \begin{align*} -\frac{1}{10 \,{\left (b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.961724, size = 63, normalized size = 3.94 \begin{align*} - \frac{1}{10 a^{5} b + 50 a^{4} b^{2} x^{2} + 100 a^{3} b^{3} x^{4} + 100 a^{2} b^{4} x^{6} + 50 a b^{5} x^{8} + 10 b^{6} x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15108, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{10 \,{\left (b x^{2} + a\right )}^{5} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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