Optimal. Leaf size=54 \[ -\frac {a^4}{9 x^9}-\frac {4 a^3 b}{7 x^7}-\frac {6 a^2 b^2}{5 x^5}-\frac {4 a b^3}{3 x^3}-\frac {b^4}{x} \]
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Rubi [A]
time = 0.02, antiderivative size = 54, 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, 276}
\begin {gather*} -\frac {a^4}{9 x^9}-\frac {4 a^3 b}{7 x^7}-\frac {6 a^2 b^2}{5 x^5}-\frac {4 a b^3}{3 x^3}-\frac {b^4}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{10}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^4}{x^{10}} \, dx}{b^4}\\ &=\frac {\int \left (\frac {a^4 b^4}{x^{10}}+\frac {4 a^3 b^5}{x^8}+\frac {6 a^2 b^6}{x^6}+\frac {4 a b^7}{x^4}+\frac {b^8}{x^2}\right ) \, dx}{b^4}\\ &=-\frac {a^4}{9 x^9}-\frac {4 a^3 b}{7 x^7}-\frac {6 a^2 b^2}{5 x^5}-\frac {4 a b^3}{3 x^3}-\frac {b^4}{x}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 54, normalized size = 1.00 \begin {gather*} -\frac {a^4}{9 x^9}-\frac {4 a^3 b}{7 x^7}-\frac {6 a^2 b^2}{5 x^5}-\frac {4 a b^3}{3 x^3}-\frac {b^4}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 47, normalized size = 0.87
method | result | size |
default | \(-\frac {a^{4}}{9 x^{9}}-\frac {4 a^{3} b}{7 x^{7}}-\frac {6 a^{2} b^{2}}{5 x^{5}}-\frac {4 a \,b^{3}}{3 x^{3}}-\frac {b^{4}}{x}\) | \(47\) |
norman | \(\frac {-b^{4} x^{8}-\frac {4}{3} a \,b^{3} x^{6}-\frac {6}{5} a^{2} b^{2} x^{4}-\frac {4}{7} a^{3} b \,x^{2}-\frac {1}{9} a^{4}}{x^{9}}\) | \(48\) |
risch | \(\frac {-b^{4} x^{8}-\frac {4}{3} a \,b^{3} x^{6}-\frac {6}{5} a^{2} b^{2} x^{4}-\frac {4}{7} a^{3} b \,x^{2}-\frac {1}{9} a^{4}}{x^{9}}\) | \(48\) |
gosper | \(-\frac {315 b^{4} x^{8}+420 a \,b^{3} x^{6}+378 a^{2} b^{2} x^{4}+180 a^{3} b \,x^{2}+35 a^{4}}{315 x^{9}}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 48, normalized size = 0.89 \begin {gather*} -\frac {315 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 378 \, a^{2} b^{2} x^{4} + 180 \, a^{3} b x^{2} + 35 \, a^{4}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 48, normalized size = 0.89 \begin {gather*} -\frac {315 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 378 \, a^{2} b^{2} x^{4} + 180 \, a^{3} b x^{2} + 35 \, a^{4}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 51, normalized size = 0.94 \begin {gather*} \frac {- 35 a^{4} - 180 a^{3} b x^{2} - 378 a^{2} b^{2} x^{4} - 420 a b^{3} x^{6} - 315 b^{4} x^{8}}{315 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.38, size = 48, normalized size = 0.89 \begin {gather*} -\frac {315 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 378 \, a^{2} b^{2} x^{4} + 180 \, a^{3} b x^{2} + 35 \, a^{4}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 47, normalized size = 0.87 \begin {gather*} -\frac {\frac {a^4}{9}+\frac {4\,a^3\,b\,x^2}{7}+\frac {6\,a^2\,b^2\,x^4}{5}+\frac {4\,a\,b^3\,x^6}{3}+b^4\,x^8}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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