Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^6}{12 a x^{12}} \]
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Rubi [A] time = 0.0035702, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\left (a+b x^2\right )^6}{12 a x^{12}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^5}{x^{13}} \, dx &=-\frac{\left (a+b x^2\right )^6}{12 a x^{12}}\\ \end{align*}
Mathematica [B] time = 0.0040731, size = 69, normalized size = 3.63 \[ -\frac{5 a^3 b^2}{4 x^8}-\frac{5 a^2 b^3}{3 x^6}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{12 x^{12}}-\frac{5 a b^4}{4 x^4}-\frac{b^5}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, size = 58, normalized size = 3.1 \begin{align*} -{\frac{5\,{a}^{3}{b}^{2}}{4\,{x}^{8}}}-{\frac{{a}^{4}b}{2\,{x}^{10}}}-{\frac{{a}^{5}}{12\,{x}^{12}}}-{\frac{5\,a{b}^{4}}{4\,{x}^{4}}}-{\frac{{b}^{5}}{2\,{x}^{2}}}-{\frac{5\,{a}^{2}{b}^{3}}{3\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.40163, size = 77, normalized size = 4.05 \begin{align*} -\frac{6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.25478, size = 127, normalized size = 6.68 \begin{align*} -\frac{6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.6015, size = 61, normalized size = 3.21 \begin{align*} - \frac{a^{5} + 6 a^{4} b x^{2} + 15 a^{3} b^{2} x^{4} + 20 a^{2} b^{3} x^{6} + 15 a b^{4} x^{8} + 6 b^{5} x^{10}}{12 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 2.87239, size = 77, normalized size = 4.05 \begin{align*} -\frac{6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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