Optimal. Leaf size=77 \[ -\frac {a^6}{10 x^{10}}-\frac {3 a^5 b}{4 x^8}-\frac {5 a^4 b^2}{2 x^6}-\frac {5 a^3 b^3}{x^4}-\frac {15 a^2 b^4}{2 x^2}+6 a b^5 \log (x)+\frac {b^6 x^2}{2} \]
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Rubi [A] time = 0.05, antiderivative size = 77, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {28, 266, 43} \begin {gather*} -\frac {5 a^4 b^2}{2 x^6}-\frac {5 a^3 b^3}{x^4}-\frac {15 a^2 b^4}{2 x^2}-\frac {3 a^5 b}{4 x^8}-\frac {a^6}{10 x^{10}}+6 a b^5 \log (x)+\frac {b^6 x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^3}{x^{11}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^6}{x^{11}} \, dx}{b^6}\\ &=\frac {\operatorname {Subst}\left (\int \frac {\left (a b+b^2 x\right )^6}{x^6} \, dx,x,x^2\right )}{2 b^6}\\ &=\frac {\operatorname {Subst}\left (\int \left (b^{12}+\frac {a^6 b^6}{x^6}+\frac {6 a^5 b^7}{x^5}+\frac {15 a^4 b^8}{x^4}+\frac {20 a^3 b^9}{x^3}+\frac {15 a^2 b^{10}}{x^2}+\frac {6 a b^{11}}{x}\right ) \, dx,x,x^2\right )}{2 b^6}\\ &=-\frac {a^6}{10 x^{10}}-\frac {3 a^5 b}{4 x^8}-\frac {5 a^4 b^2}{2 x^6}-\frac {5 a^3 b^3}{x^4}-\frac {15 a^2 b^4}{2 x^2}+\frac {b^6 x^2}{2}+6 a b^5 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 77, normalized size = 1.00 \begin {gather*} -\frac {a^6}{10 x^{10}}-\frac {3 a^5 b}{4 x^8}-\frac {5 a^4 b^2}{2 x^6}-\frac {5 a^3 b^3}{x^4}-\frac {15 a^2 b^4}{2 x^2}+6 a b^5 \log (x)+\frac {b^6 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 (a^2+2 a b x^2+b^2 x^4\right )^3}{x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.53, size = 72, normalized size = 0.94 \begin {gather*} \frac {10 \, b^{6} x^{12} + 120 \, a b^{5} x^{10} \log \relax (x) - 150 \, a^{2} b^{4} x^{8} - 100 \, a^{3} b^{3} x^{6} - 50 \, a^{4} b^{2} x^{4} - 15 \, a^{5} b x^{2} - 2 \, a^{6}}{20 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 81, normalized size = 1.05 \begin {gather*} \frac {1}{2} \, b^{6} x^{2} + 3 \, a b^{5} \log \left (x^{2}\right ) - \frac {137 \, a b^{5} x^{10} + 150 \, a^{2} b^{4} x^{8} + 100 \, a^{3} b^{3} x^{6} + 50 \, a^{4} b^{2} x^{4} + 15 \, a^{5} b x^{2} + 2 \, a^{6}}{20 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 68, normalized size = 0.88 \begin {gather*} \frac {b^{6} x^{2}}{2}+6 a \,b^{5} \ln \relax (x )-\frac {15 a^{2} b^{4}}{2 x^{2}}-\frac {5 a^{3} b^{3}}{x^{4}}-\frac {5 a^{4} b^{2}}{2 x^{6}}-\frac {3 a^{5} b}{4 x^{8}}-\frac {a^{6}}{10 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 72, normalized size = 0.94 \begin {gather*} \frac {1}{2} \, b^{6} x^{2} + 3 \, a b^{5} \log \left (x^{2}\right ) - \frac {150 \, a^{2} b^{4} x^{8} + 100 \, a^{3} b^{3} x^{6} + 50 \, a^{4} b^{2} x^{4} + 15 \, a^{5} b x^{2} + 2 \, a^{6}}{20 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.40, size = 70, normalized size = 0.91 \begin {gather*} \frac {b^6\,x^2}{2}-\frac {\frac {a^6}{10}+\frac {3\,a^5\,b\,x^2}{4}+\frac {5\,a^4\,b^2\,x^4}{2}+5\,a^3\,b^3\,x^6+\frac {15\,a^2\,b^4\,x^8}{2}}{x^{10}}+6\,a\,b^5\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.63, size = 75, normalized size = 0.97 \begin {gather*} 6 a b^{5} \log {\relax (x )} + \frac {b^{6} x^{2}}{2} + \frac {- 2 a^{6} - 15 a^{5} b x^{2} - 50 a^{4} b^{2} x^{4} - 100 a^{3} b^{3} x^{6} - 150 a^{2} b^{4} x^{8}}{20 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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