Optimal. Leaf size=14 \[ -\frac{1}{14 b (a+b x)^{14}} \]
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Rubi [A] time = 0.0181846, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 51, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.039, Rules used = {2058, 32} \[ -\frac{1}{14 b (a+b x)^{14}} \]
Antiderivative was successfully verified.
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Rule 2058
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right )^3} \, dx &=\int \frac{1}{(a+b x)^{15}} \, dx\\ &=-\frac{1}{14 b (a+b x)^{14}}\\ \end{align*}
Mathematica [A] time = 0.0039681, size = 14, normalized size = 1. \[ -\frac{1}{14 b (a+b x)^{14}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{14\,b \left ( bx+a \right ) ^{14}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.66979, size = 211, normalized size = 15.07 \begin{align*} -\frac{1}{14 \,{\left (b^{15} x^{14} + 14 \, a b^{14} x^{13} + 91 \, a^{2} b^{13} x^{12} + 364 \, a^{3} b^{12} x^{11} + 1001 \, a^{4} b^{11} x^{10} + 2002 \, a^{5} b^{10} x^{9} + 3003 \, a^{6} b^{9} x^{8} + 3432 \, a^{7} b^{8} x^{7} + 3003 \, a^{8} b^{7} x^{6} + 2002 \, a^{9} b^{6} x^{5} + 1001 \, a^{10} b^{5} x^{4} + 364 \, a^{11} b^{4} x^{3} + 91 \, a^{12} b^{3} x^{2} + 14 \, a^{13} b^{2} x + a^{14} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.76439, size = 370, normalized size = 26.43 \begin{align*} -\frac{1}{14 \,{\left (b^{15} x^{14} + 14 \, a b^{14} x^{13} + 91 \, a^{2} b^{13} x^{12} + 364 \, a^{3} b^{12} x^{11} + 1001 \, a^{4} b^{11} x^{10} + 2002 \, a^{5} b^{10} x^{9} + 3003 \, a^{6} b^{9} x^{8} + 3432 \, a^{7} b^{8} x^{7} + 3003 \, a^{8} b^{7} x^{6} + 2002 \, a^{9} b^{6} x^{5} + 1001 \, a^{10} b^{5} x^{4} + 364 \, a^{11} b^{4} x^{3} + 91 \, a^{12} b^{3} x^{2} + 14 \, a^{13} b^{2} x + a^{14} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.55131, size = 168, normalized size = 12. \begin{align*} - \frac{1}{14 a^{14} b + 196 a^{13} b^{2} x + 1274 a^{12} b^{3} x^{2} + 5096 a^{11} b^{4} x^{3} + 14014 a^{10} b^{5} x^{4} + 28028 a^{9} b^{6} x^{5} + 42042 a^{8} b^{7} x^{6} + 48048 a^{7} b^{8} x^{7} + 42042 a^{6} b^{9} x^{8} + 28028 a^{5} b^{10} x^{9} + 14014 a^{4} b^{11} x^{10} + 5096 a^{3} b^{12} x^{11} + 1274 a^{2} b^{13} x^{12} + 196 a b^{14} x^{13} + 14 b^{15} x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14627, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{14 \,{\left (b x + a\right )}^{14} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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