Optimal. Leaf size=14 \[ -\frac{1}{9 b (a+b x)^9} \]
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Rubi [A] time = 0.0167872, 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} \[ -\frac{1}{9 b (a+b x)^9} \]
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 )^2} \, dx &=\int \frac{1}{(a+b x)^{10}} \, dx\\ &=-\frac{1}{9 b (a+b x)^9}\\ \end{align*}
Mathematica [A] time = 0.0035355, size = 14, normalized size = 1. \[ -\frac{1}{9 b (a+b x)^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{9\,b \left ( bx+a \right ) ^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.26305, size = 136, normalized size = 9.71 \begin{align*} -\frac{1}{9 \,{\left (b^{10} x^{9} + 9 \, a b^{9} x^{8} + 36 \, a^{2} b^{8} x^{7} + 84 \, a^{3} b^{7} x^{6} + 126 \, a^{4} b^{6} x^{5} + 126 \, a^{5} b^{5} x^{4} + 84 \, a^{6} b^{4} x^{3} + 36 \, a^{7} b^{3} x^{2} + 9 \, a^{8} b^{2} x + a^{9} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.62422, size = 212, normalized size = 15.14 \begin{align*} -\frac{1}{9 \,{\left (b^{10} x^{9} + 9 \, a b^{9} x^{8} + 36 \, a^{2} b^{8} x^{7} + 84 \, a^{3} b^{7} x^{6} + 126 \, a^{4} b^{6} x^{5} + 126 \, a^{5} b^{5} x^{4} + 84 \, a^{6} b^{4} x^{3} + 36 \, a^{7} b^{3} x^{2} + 9 \, a^{8} b^{2} x + a^{9} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.840877, size = 109, normalized size = 7.79 \begin{align*} - \frac{1}{9 a^{9} b + 81 a^{8} b^{2} x + 324 a^{7} b^{3} x^{2} + 756 a^{6} b^{4} x^{3} + 1134 a^{5} b^{5} x^{4} + 1134 a^{4} b^{6} x^{5} + 756 a^{3} b^{7} x^{6} + 324 a^{2} b^{8} x^{7} + 81 a b^{9} x^{8} + 9 b^{10} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13431, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{9 \,{\left (b x + a\right )}^{9} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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