Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^5}{10 a x^{10}} \]
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Rubi [A] time = 0.0061135, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {28, 264} \[ -\frac{\left (a+b x^2\right )^5}{10 a x^{10}} \]
Antiderivative was successfully verified.
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Rule 28
Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{11}} \, dx &=\frac{\int \frac{\left (a b+b^2 x^2\right )^4}{x^{11}} \, dx}{b^4}\\ &=-\frac{\left (a+b x^2\right )^5}{10 a x^{10}}\\ \end{align*}
Mathematica [B] time = 0.0041784, size = 52, normalized size = 2.74 \[ -\frac{a^2 b^2}{x^6}-\frac{a^3 b}{2 x^8}-\frac{a^4}{10 x^{10}}-\frac{a b^3}{x^4}-\frac{b^4}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.048, size = 47, normalized size = 2.5 \begin{align*} -{\frac{{a}^{4}}{10\,{x}^{10}}}-{\frac{a{b}^{3}}{{x}^{4}}}-{\frac{{b}^{4}}{2\,{x}^{2}}}-{\frac{{a}^{3}b}{2\,{x}^{8}}}-{\frac{{b}^{2}{a}^{2}}{{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.993977, size = 62, normalized size = 3.26 \begin{align*} -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.6613, size = 103, normalized size = 5.42 \begin{align*} -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.506714, size = 49, normalized size = 2.58 \begin{align*} - \frac{a^{4} + 5 a^{3} b x^{2} + 10 a^{2} b^{2} x^{4} + 10 a b^{3} x^{6} + 5 b^{4} x^{8}}{10 x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.20888, size = 62, normalized size = 3.26 \begin{align*} -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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