Optimal. Leaf size=39 \[ -\frac {b^3}{6 x^6}-\frac {3 b^2 c}{4 x^4}-\frac {3 b c^2}{2 x^2}+c^3 \log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {1584, 266, 43} \begin {gather*} -\frac {3 b^2 c}{4 x^4}-\frac {b^3}{6 x^6}-\frac {3 b c^2}{2 x^2}+c^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^3}{x^{13}} \, dx &=\int \frac {\left (b+c x^2\right )^3}{x^7} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(b+c x)^3}{x^4} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {b^3}{x^4}+\frac {3 b^2 c}{x^3}+\frac {3 b c^2}{x^2}+\frac {c^3}{x}\right ) \, dx,x,x^2\right )\\ &=-\frac {b^3}{6 x^6}-\frac {3 b^2 c}{4 x^4}-\frac {3 b c^2}{2 x^2}+c^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \begin {gather*} -\frac {b^3}{6 x^6}-\frac {3 b^2 c}{4 x^4}-\frac {3 b c^2}{2 x^2}+c^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 (b x^2+c x^4\right )^3}{x^{13}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.65, size = 39, normalized size = 1.00 \begin {gather*} \frac {12 \, c^{3} x^{6} \log \relax (x) - 18 \, b c^{2} x^{4} - 9 \, b^{2} c x^{2} - 2 \, b^{3}}{12 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 47, normalized size = 1.21 \begin {gather*} \frac {1}{2} \, c^{3} \log \left (x^{2}\right ) - \frac {11 \, c^{3} x^{6} + 18 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} + 2 \, b^{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*} c^{3} \ln \relax (x )-\frac {3 b \,c^{2}}{2 x^{2}}-\frac {3 b^{2} c}{4 x^{4}}-\frac {b^{3}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 39, normalized size = 1.00 \begin {gather*} \frac {1}{2} \, c^{3} \log \left (x^{2}\right ) - \frac {18 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} + 2 \, b^{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*} c^3\,\ln \relax (x)-\frac {\frac {b^3}{6}+\frac {3\,b^2\,c\,x^2}{4}+\frac {3\,b\,c^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 = 0.29, size = 37, normalized size = 0.95 \begin {gather*} c^{3} \log {\relax (x )} + \frac {- 2 b^{3} - 9 b^{2} c x^{2} - 18 b c^{2} x^{4}}{12 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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