Optimal. Leaf size=56 \[ -\frac{2 a^2 b^2}{3 x^9}-\frac{4 a^3 b}{11 x^{11}}-\frac{a^4}{13 x^{13}}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5} \]
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Rubi [A] time = 0.0274963, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {28, 270} \[ -\frac{2 a^2 b^2}{3 x^9}-\frac{4 a^3 b}{11 x^{11}}-\frac{a^4}{13 x^{13}}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 28
Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{14}} \, dx &=\frac{\int \frac{\left (a b+b^2 x^2\right )^4}{x^{14}} \, dx}{b^4}\\ &=\frac{\int \left (\frac{a^4 b^4}{x^{14}}+\frac{4 a^3 b^5}{x^{12}}+\frac{6 a^2 b^6}{x^{10}}+\frac{4 a b^7}{x^8}+\frac{b^8}{x^6}\right ) \, dx}{b^4}\\ &=-\frac{a^4}{13 x^{13}}-\frac{4 a^3 b}{11 x^{11}}-\frac{2 a^2 b^2}{3 x^9}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0081476, size = 56, normalized size = 1. \[ -\frac{2 a^2 b^2}{3 x^9}-\frac{4 a^3 b}{11 x^{11}}-\frac{a^4}{13 x^{13}}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 47, normalized size = 0.8 \begin{align*} -{\frac{{a}^{4}}{13\,{x}^{13}}}-{\frac{4\,{a}^{3}b}{11\,{x}^{11}}}-{\frac{2\,{b}^{2}{a}^{2}}{3\,{x}^{9}}}-{\frac{4\,a{b}^{3}}{7\,{x}^{7}}}-{\frac{{b}^{4}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97777, size = 65, normalized size = 1.16 \begin{align*} -\frac{3003 \, b^{4} x^{8} + 8580 \, a b^{3} x^{6} + 10010 \, a^{2} b^{2} x^{4} + 5460 \, a^{3} b x^{2} + 1155 \, a^{4}}{15015 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61811, size = 128, normalized size = 2.29 \begin{align*} -\frac{3003 \, b^{4} x^{8} + 8580 \, a b^{3} x^{6} + 10010 \, a^{2} b^{2} x^{4} + 5460 \, a^{3} b x^{2} + 1155 \, a^{4}}{15015 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.558685, size = 51, normalized size = 0.91 \begin{align*} - \frac{1155 a^{4} + 5460 a^{3} b x^{2} + 10010 a^{2} b^{2} x^{4} + 8580 a b^{3} x^{6} + 3003 b^{4} x^{8}}{15015 x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20116, size = 65, normalized size = 1.16 \begin{align*} -\frac{3003 \, b^{4} x^{8} + 8580 \, a b^{3} x^{6} + 10010 \, a^{2} b^{2} x^{4} + 5460 \, a^{3} b x^{2} + 1155 \, a^{4}}{15015 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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