Optimal. Leaf size=39 \[ -\frac {a^3}{6 x^6}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}+b^3 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 39, 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} \begin {gather*} -\frac {3 a^2 b}{4 x^4}-\frac {a^3}{6 x^6}-\frac {3 a b^2}{2 x^2}+b^3 \log (x) \end {gather*}
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^7} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^4} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^3}{x^4}+\frac {3 a^2 b}{x^3}+\frac {3 a b^2}{x^2}+\frac {b^3}{x}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^3}{6 x^6}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}+b^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \begin {gather*} -\frac {a^3}{6 x^6}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}+b^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^2\right )^3}{x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.02, size = 39, normalized size = 1.00 \begin {gather*} \frac {12 \, b^{3} x^{6} \log \relax (x) - 18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} - 2 \, a^{3}}{12 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 47, normalized size = 1.21 \begin {gather*} \frac {1}{2} \, b^{3} \log \left (x^{2}\right ) - \frac {11 \, b^{3} x^{6} + 18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 34, normalized size = 0.87 \begin {gather*} b^{3} \ln \relax (x )-\frac {3 a \,b^{2}}{2 x^{2}}-\frac {3 a^{2} b}{4 x^{4}}-\frac {a^{3}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 39, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, b^{3} \log \left (x^{2}\right ) - \frac {18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 36, normalized size = 0.92 \begin {gather*} b^3\,\ln \relax (x)-\frac {\frac {a^3}{6}+\frac {3\,a^2\,b\,x^2}{4}+\frac {3\,a\,b^2\,x^4}{2}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 37, normalized size = 0.95 \begin {gather*} b^{3} \log {\relax (x )} + \frac {- 2 a^{3} - 9 a^{2} b x^{2} - 18 a b^{2} x^{4}}{12 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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