Optimal. Leaf size=71 \[ -\frac {a^6}{11 x^{11}}-\frac {2 a^5 b}{3 x^9}-\frac {15 a^4 b^2}{7 x^7}-\frac {4 a^3 b^3}{x^5}-\frac {5 a^2 b^4}{x^3}-\frac {6 a b^5}{x}+b^6 x \]
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Rubi [A] time = 0.04, antiderivative size = 71, 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} \[ -\frac {15 a^4 b^2}{7 x^7}-\frac {4 a^3 b^3}{x^5}-\frac {5 a^2 b^4}{x^3}-\frac {2 a^5 b}{3 x^9}-\frac {a^6}{11 x^{11}}-\frac {6 a b^5}{x}+b^6 x \]
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 )^3}{x^{12}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^6}{x^{12}} \, dx}{b^6}\\ &=\frac {\int \left (b^{12}+\frac {a^6 b^6}{x^{12}}+\frac {6 a^5 b^7}{x^{10}}+\frac {15 a^4 b^8}{x^8}+\frac {20 a^3 b^9}{x^6}+\frac {15 a^2 b^{10}}{x^4}+\frac {6 a b^{11}}{x^2}\right ) \, dx}{b^6}\\ &=-\frac {a^6}{11 x^{11}}-\frac {2 a^5 b}{3 x^9}-\frac {15 a^4 b^2}{7 x^7}-\frac {4 a^3 b^3}{x^5}-\frac {5 a^2 b^4}{x^3}-\frac {6 a b^5}{x}+b^6 x\\ \end {align*}
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Mathematica [A] time = 0.01, size = 71, normalized size = 1.00 \[ -\frac {a^6}{11 x^{11}}-\frac {2 a^5 b}{3 x^9}-\frac {15 a^4 b^2}{7 x^7}-\frac {4 a^3 b^3}{x^5}-\frac {5 a^2 b^4}{x^3}-\frac {6 a b^5}{x}+b^6 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 70, normalized size = 0.99 \[ \frac {231 \, b^{6} x^{12} - 1386 \, a b^{5} x^{10} - 1155 \, a^{2} b^{4} x^{8} - 924 \, a^{3} b^{3} x^{6} - 495 \, a^{4} b^{2} x^{4} - 154 \, a^{5} b x^{2} - 21 \, a^{6}}{231 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 68, normalized size = 0.96 \[ b^{6} x - \frac {1386 \, a b^{5} x^{10} + 1155 \, a^{2} b^{4} x^{8} + 924 \, a^{3} b^{3} x^{6} + 495 \, a^{4} b^{2} x^{4} + 154 \, a^{5} b x^{2} + 21 \, a^{6}}{231 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 66, normalized size = 0.93 \[ b^{6} x -\frac {6 a \,b^{5}}{x}-\frac {5 a^{2} b^{4}}{x^{3}}-\frac {4 a^{3} b^{3}}{x^{5}}-\frac {15 a^{4} b^{2}}{7 x^{7}}-\frac {2 a^{5} b}{3 x^{9}}-\frac {a^{6}}{11 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 68, normalized size = 0.96 \[ b^{6} x - \frac {1386 \, a b^{5} x^{10} + 1155 \, a^{2} b^{4} x^{8} + 924 \, a^{3} b^{3} x^{6} + 495 \, a^{4} b^{2} x^{4} + 154 \, a^{5} b x^{2} + 21 \, a^{6}}{231 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.30, size = 68, normalized size = 0.96 \[ b^6\,x-\frac {\frac {a^6}{11}+\frac {2\,a^5\,b\,x^2}{3}+\frac {15\,a^4\,b^2\,x^4}{7}+4\,a^3\,b^3\,x^6+5\,a^2\,b^4\,x^8+6\,a\,b^5\,x^{10}}{x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.52, size = 71, normalized size = 1.00 \[ b^{6} x + \frac {- 21 a^{6} - 154 a^{5} b x^{2} - 495 a^{4} b^{2} x^{4} - 924 a^{3} b^{3} x^{6} - 1155 a^{2} b^{4} x^{8} - 1386 a b^{5} x^{10}}{231 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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