Optimal. Leaf size=43 \[ -\frac {a^3}{12 x^{12}}-\frac {3 a^2 b}{10 x^{10}}-\frac {3 a b^2}{8 x^8}-\frac {b^3}{6 x^6} \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac {3 a^2 b}{10 x^{10}}-\frac {a^3}{12 x^{12}}-\frac {3 a b^2}{8 x^8}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^3}{x^{13}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^7} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^3}{x^7}+\frac {3 a^2 b}{x^6}+\frac {3 a b^2}{x^5}+\frac {b^3}{x^4}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^3}{12 x^{12}}-\frac {3 a^2 b}{10 x^{10}}-\frac {3 a b^2}{8 x^8}-\frac {b^3}{6 x^6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ -\frac {a^3}{12 x^{12}}-\frac {3 a^2 b}{10 x^{10}}-\frac {3 a b^2}{8 x^8}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ -\frac {b^{3}}{6 x^{6}}-\frac {3 a \,b^{2}}{8 x^{8}}-\frac {3 a^{2} b}{10 x^{10}}-\frac {a^{3}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 37, normalized size = 0.86 \[ -\frac {20 \, b^{3} x^{6} + 45 \, a b^{2} x^{4} + 36 \, a^{2} b x^{2} + 10 \, a^{3}}{120 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 37, normalized size = 0.86 \[ -\frac {\frac {a^3}{12}+\frac {3\,a^2\,b\,x^2}{10}+\frac {3\,a\,b^2\,x^4}{8}+\frac {b^3\,x^6}{6}}{x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 39, normalized size = 0.91 \[ \frac {- 10 a^{3} - 36 a^{2} b x^{2} - 45 a b^{2} x^{4} - 20 b^{3} x^{6}}{120 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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