Optimal. Leaf size=56 \[ -\frac {a^4}{11 x^{11}}-\frac {4 a^3 b}{9 x^9}-\frac {6 a^2 b^2}{7 x^7}-\frac {4 a b^3}{5 x^5}-\frac {b^4}{3 x^3} \]
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Rubi [A] time = 0.03, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {28, 270} \begin {gather*} -\frac {6 a^2 b^2}{7 x^7}-\frac {4 a^3 b}{9 x^9}-\frac {a^4}{11 x^{11}}-\frac {4 a b^3}{5 x^5}-\frac {b^4}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{12}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^4}{x^{12}} \, dx}{b^4}\\ &=\frac {\int \left (\frac {a^4 b^4}{x^{12}}+\frac {4 a^3 b^5}{x^{10}}+\frac {6 a^2 b^6}{x^8}+\frac {4 a b^7}{x^6}+\frac {b^8}{x^4}\right ) \, dx}{b^4}\\ &=-\frac {a^4}{11 x^{11}}-\frac {4 a^3 b}{9 x^9}-\frac {6 a^2 b^2}{7 x^7}-\frac {4 a b^3}{5 x^5}-\frac {b^4}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 56, normalized size = 1.00 \begin {gather*} -\frac {a^4}{11 x^{11}}-\frac {4 a^3 b}{9 x^9}-\frac {6 a^2 b^2}{7 x^7}-\frac {4 a b^3}{5 x^5}-\frac {b^4}{3 x^3} \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 )^2}{x^{12}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.66, size = 48, normalized size = 0.86 \begin {gather*} -\frac {1155 \, b^{4} x^{8} + 2772 \, a b^{3} x^{6} + 2970 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} + 315 \, a^{4}}{3465 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 48, normalized size = 0.86 \begin {gather*} -\frac {1155 \, b^{4} x^{8} + 2772 \, a b^{3} x^{6} + 2970 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} + 315 \, a^{4}}{3465 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 47, normalized size = 0.84 \begin {gather*} -\frac {b^{4}}{3 x^{3}}-\frac {4 a \,b^{3}}{5 x^{5}}-\frac {6 a^{2} b^{2}}{7 x^{7}}-\frac {4 a^{3} b}{9 x^{9}}-\frac {a^{4}}{11 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 48, normalized size = 0.86 \begin {gather*} -\frac {1155 \, b^{4} x^{8} + 2772 \, a b^{3} x^{6} + 2970 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} + 315 \, a^{4}}{3465 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.84, size = 48, normalized size = 0.86 \begin {gather*} -\frac {\frac {a^4}{11}+\frac {4\,a^3\,b\,x^2}{9}+\frac {6\,a^2\,b^2\,x^4}{7}+\frac {4\,a\,b^3\,x^6}{5}+\frac {b^4\,x^8}{3}}{x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 51, normalized size = 0.91 \begin {gather*} \frac {- 315 a^{4} - 1540 a^{3} b x^{2} - 2970 a^{2} b^{2} x^{4} - 2772 a b^{3} x^{6} - 1155 b^{4} x^{8}}{3465 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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