Optimal. Leaf size=40 \[ -\frac {b^3}{4 x^4}-\frac {3 b^2 c}{2 x^2}+3 b c^2 \log (x)+\frac {c^3 x^2}{2} \]
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Rubi [A] time = 0.03, antiderivative size = 40, 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}{2 x^2}-\frac {b^3}{4 x^4}+3 b c^2 \log (x)+\frac {c^3 x^2}{2} \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^{11}} \, dx &=\int \frac {\left (b+c x^2\right )^3}{x^5} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(b+c x)^3}{x^3} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (c^3+\frac {b^3}{x^3}+\frac {3 b^2 c}{x^2}+\frac {3 b c^2}{x}\right ) \, dx,x,x^2\right )\\ &=-\frac {b^3}{4 x^4}-\frac {3 b^2 c}{2 x^2}+\frac {c^3 x^2}{2}+3 b c^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 40, normalized size = 1.00 \begin {gather*} -\frac {b^3}{4 x^4}-\frac {3 b^2 c}{2 x^2}+3 b c^2 \log (x)+\frac {c^3 x^2}{2} \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^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.60, size = 39, normalized size = 0.98 \begin {gather*} \frac {2 \, c^{3} x^{6} + 12 \, b c^{2} x^{4} \log \relax (x) - 6 \, b^{2} c x^{2} - b^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 46, normalized size = 1.15 \begin {gather*} \frac {1}{2} \, c^{3} x^{2} + \frac {3}{2} \, b c^{2} \log \left (x^{2}\right ) - \frac {9 \, b c^{2} x^{4} + 6 \, b^{2} c x^{2} + b^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 35, normalized size = 0.88 \begin {gather*} \frac {c^{3} x^{2}}{2}+3 b \,c^{2} \ln \relax (x )-\frac {3 b^{2} c}{2 x^{2}}-\frac {b^{3}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 37, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, c^{3} x^{2} + \frac {3}{2} \, b c^{2} \log \left (x^{2}\right ) - \frac {6 \, b^{2} c x^{2} + b^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.92 \begin {gather*} \frac {c^3\,x^2}{2}-\frac {\frac {b^3}{4}+\frac {3\,c\,b^2\,x^2}{2}}{x^4}+3\,b\,c^2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 37, normalized size = 0.92 \begin {gather*} 3 b c^{2} \log {\relax (x )} + \frac {c^{3} x^{2}}{2} + \frac {- b^{3} - 6 b^{2} c x^{2}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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