Optimal. Leaf size=40 \[ -\frac {a^3}{6 x^6}+\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}-b^3 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {266, 43} \[ \frac {3 a^2 b}{4 x^4}-\frac {a^3}{6 x^6}-\frac {3 a b^2}{2 x^2}-b^3 \log (x) \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a-b x^2\right )^3}{x^7} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a-b x)^3}{x^4} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^3}{x^4}-\frac {3 a^2 b}{x^3}+\frac {3 a b^2}{x^2}-\frac {b^3}{x}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^3}{6 x^6}+\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}-b^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 40, normalized size = 1.00 \[ -\frac {a^3}{6 x^6}+\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{2 x^2}-b^3 \log (x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 37, normalized size = 0.92 \[ b^3 (-\log (x))-\frac {a \left (2 a^2-9 a b x^2+18 b^2 x^4\right )}{12 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.22, size = 39, normalized size = 0.98 \[ -\frac {12 \, b^{3} x^{6} \log \relax (x) + 18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 47, normalized size = 1.18 \[ -\frac {1}{2} \, b^{3} \log \left (x^{2}\right ) + \frac {11 \, b^{3} x^{6} - 18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} - 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 35, normalized size = 0.88
method | result | size |
default | \(-\frac {a^{3}}{6 x^{6}}+\frac {3 a^{2} b}{4 x^{4}}-\frac {3 a \,b^{2}}{2 x^{2}}-b^{3} \ln \relax (x )\) | \(35\) |
norman | \(\frac {-\frac {1}{6} a^{3}+\frac {3}{4} a^{2} b \,x^{2}-\frac {3}{2} b^{2} a \,x^{4}}{x^{6}}-b^{3} \ln \relax (x )\) | \(37\) |
risch | \(\frac {-\frac {1}{6} a^{3}+\frac {3}{4} a^{2} b \,x^{2}-\frac {3}{2} b^{2} a \,x^{4}}{x^{6}}-b^{3} \ln \relax (x )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 39, normalized size = 0.98 \[ -\frac {1}{2} \, b^{3} \log \left (x^{2}\right ) - \frac {18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 37, normalized size = 0.92 \[ -b^3\,\ln \relax (x)-\frac {\frac {a^3}{6}-\frac {3\,a^2\,b\,x^2}{4}+\frac {3\,a\,b^2\,x^4}{2}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 37, normalized size = 0.92 \[ - b^{3} \log {\relax (x )} - \frac {2 a^{3} - 9 a^{2} b x^{2} + 18 a b^{2} x^{4}}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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