Optimal. Leaf size=14 \[ -\frac {1}{9 b (a+b x)^9} \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, 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 32
Rule 2058
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*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {1}{9 b (a+b x)^9} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.62, size = 101, normalized size = 7.21 \[ -\frac {1}{9 \, {\left (b^{10} x^{9} + 9 \, a b^{9} x^{8} + 36 \, a^{2} b^{8} x^{7} + 84 \, a^{3} b^{7} x^{6} + 126 \, a^{4} b^{6} x^{5} + 126 \, a^{5} b^{5} x^{4} + 84 \, a^{6} b^{4} x^{3} + 36 \, a^{7} b^{3} x^{2} + 9 \, a^{8} b^{2} x + a^{9} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 12, normalized size = 0.86 \[ -\frac {1}{9 \, {\left (b x + a\right )}^{9} b} \]
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 \[ -\frac {1}{9 \left (b x +a \right )^{9} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.60, size = 101, normalized size = 7.21 \[ -\frac {1}{9 \, {\left (b^{10} x^{9} + 9 \, a b^{9} x^{8} + 36 \, a^{2} b^{8} x^{7} + 84 \, a^{3} b^{7} x^{6} + 126 \, a^{4} b^{6} x^{5} + 126 \, a^{5} b^{5} x^{4} + 84 \, a^{6} b^{4} x^{3} + 36 \, a^{7} b^{3} x^{2} + 9 \, a^{8} b^{2} x + a^{9} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.10, size = 103, normalized size = 7.36 \[ -\frac {1}{9\,a^9\,b+81\,a^8\,b^2\,x+324\,a^7\,b^3\,x^2+756\,a^6\,b^4\,x^3+1134\,a^5\,b^5\,x^4+1134\,a^4\,b^6\,x^5+756\,a^3\,b^7\,x^6+324\,a^2\,b^8\,x^7+81\,a\,b^9\,x^8+9\,b^{10}\,x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.59, size = 109, normalized size = 7.79 \[ - \frac {1}{9 a^{9} b + 81 a^{8} b^{2} x + 324 a^{7} b^{3} x^{2} + 756 a^{6} b^{4} x^{3} + 1134 a^{5} b^{5} x^{4} + 1134 a^{4} b^{6} x^{5} + 756 a^{3} b^{7} x^{6} + 324 a^{2} b^{8} x^{7} + 81 a b^{9} x^{8} + 9 b^{10} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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