Optimal. Leaf size=14 \[ -\frac {1}{8 b (a+b x)^8} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2058, 32} \[ -\frac {1}{8 b (a+b x)^8} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2058
Rubi steps
\begin {align*} \int \frac {1}{\left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^3} \, dx &=\int \frac {1}{(a+b x)^9} \, dx\\ &=-\frac {1}{8 b (a+b x)^8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {1}{8 b (a+b x)^8} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.83, size = 90, normalized size = 6.43 \[ -\frac {1}{8 \, {\left (b^{9} x^{8} + 8 \, a b^{8} x^{7} + 28 \, a^{2} b^{7} x^{6} + 56 \, a^{3} b^{6} x^{5} + 70 \, a^{4} b^{5} x^{4} + 56 \, a^{5} b^{4} x^{3} + 28 \, a^{6} b^{3} x^{2} + 8 \, a^{7} b^{2} x + a^{8} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 12, normalized size = 0.86 \[ -\frac {1}{8 \, {\left (b x + a\right )}^{8} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ -\frac {1}{8 \left (b x +a \right )^{8} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 90, normalized size = 6.43 \[ -\frac {1}{8 \, {\left (b^{9} x^{8} + 8 \, a b^{8} x^{7} + 28 \, a^{2} b^{7} x^{6} + 56 \, a^{3} b^{6} x^{5} + 70 \, a^{4} b^{5} x^{4} + 56 \, a^{5} b^{4} x^{3} + 28 \, a^{6} b^{3} x^{2} + 8 \, a^{7} b^{2} x + a^{8} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.07, size = 92, normalized size = 6.57 \[ -\frac {1}{8\,a^8\,b+64\,a^7\,b^2\,x+224\,a^6\,b^3\,x^2+448\,a^5\,b^4\,x^3+560\,a^4\,b^5\,x^4+448\,a^3\,b^6\,x^5+224\,a^2\,b^7\,x^6+64\,a\,b^8\,x^7+8\,b^9\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.54, size = 97, normalized size = 6.93 \[ - \frac {1}{8 a^{8} b + 64 a^{7} b^{2} x + 224 a^{6} b^{3} x^{2} + 448 a^{5} b^{4} x^{3} + 560 a^{4} b^{5} x^{4} + 448 a^{3} b^{6} x^{5} + 224 a^{2} b^{7} x^{6} + 64 a b^{8} x^{7} + 8 b^{9} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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