Optimal. Leaf size=28 \[ -\frac {1-3 a x}{24 a^3 (1-a x)^6 (a x+1)^3} \]
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Rubi [A] time = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {81} \[ -\frac {1-3 a x}{24 a^3 (1-a x)^6 (a x+1)^3} \]
Antiderivative was successfully verified.
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Rule 81
Rubi steps
\begin {align*} \int \frac {x^2}{(1-a x)^7 (1+a x)^4} \, dx &=-\frac {1-3 a x}{24 a^3 (1-a x)^6 (1+a x)^3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 27, normalized size = 0.96 \[ \frac {3 a x-1}{24 a^3 (a x-1)^6 (a x+1)^3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.84, size = 67, normalized size = 2.39 \[ \frac {3 \, a x - 1}{24 \, {\left (a^{12} x^{9} - 3 \, a^{11} x^{8} + 8 \, a^{9} x^{6} - 6 \, a^{8} x^{5} - 6 \, a^{7} x^{4} + 8 \, a^{6} x^{3} - 3 \, a^{4} x + a^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.16, size = 77, normalized size = 2.75 \[ -\frac {12 \, a^{2} x^{2} + 33 \, a x + 25}{1536 \, {\left (a x + 1\right )}^{3} a^{3}} + \frac {12 \, a^{5} x^{5} - 75 \, a^{4} x^{4} + 196 \, a^{3} x^{3} - 270 \, a^{2} x^{2} + 192 \, a x - 39}{1536 \, {\left (a x - 1\right )}^{6} a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 98, normalized size = 3.50 \[ -\frac {1}{384 \left (a x +1\right )^{3} a^{3}}-\frac {3}{512 \left (a x +1\right )^{2} a^{3}}-\frac {1}{128 \left (a x +1\right ) a^{3}}+\frac {1}{96 \left (a x -1\right )^{6} a^{3}}+\frac {1}{96 \left (a x -1\right )^{3} a^{3}}-\frac {5}{512 \left (a x -1\right )^{2} a^{3}}+\frac {1}{128 \left (a x -1\right ) a^{3}}-\frac {1}{128 \left (a x -1\right )^{4} a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.63, size = 67, normalized size = 2.39 \[ \frac {3 \, a x - 1}{24 \, {\left (a^{12} x^{9} - 3 \, a^{11} x^{8} + 8 \, a^{9} x^{6} - 6 \, a^{8} x^{5} - 6 \, a^{7} x^{4} + 8 \, a^{6} x^{3} - 3 \, a^{4} x + a^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.52, size = 70, normalized size = 2.50 \[ -\frac {\frac {x}{8\,a^2}-\frac {1}{24\,a^3}}{-a^9\,x^9+3\,a^8\,x^8-8\,a^6\,x^6+6\,a^5\,x^5+6\,a^4\,x^4-8\,a^3\,x^3+3\,a\,x-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.63, size = 70, normalized size = 2.50 \[ - \frac {- 3 a x + 1}{24 a^{12} x^{9} - 72 a^{11} x^{8} + 192 a^{9} x^{6} - 144 a^{8} x^{5} - 144 a^{7} x^{4} + 192 a^{6} x^{3} - 72 a^{4} x + 24 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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