Optimal. Leaf size=36 \[ -\frac{1}{2 x^2}+\frac{8}{3 x^3}-\frac{11}{2 x^4}+\frac{24}{5 x^5}-\frac{3}{2 x^6} \]
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Rubi [A] time = 0.0116563, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {698} \[ -\frac{1}{2 x^2}+\frac{8}{3 x^3}-\frac{11}{2 x^4}+\frac{24}{5 x^5}-\frac{3}{2 x^6} \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin{align*} \int \frac{\left (3-4 x+x^2\right )^2}{x^7} \, dx &=\int \left (\frac{9}{x^7}-\frac{24}{x^6}+\frac{22}{x^5}-\frac{8}{x^4}+\frac{1}{x^3}\right ) \, dx\\ &=-\frac{3}{2 x^6}+\frac{24}{5 x^5}-\frac{11}{2 x^4}+\frac{8}{3 x^3}-\frac{1}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0006213, size = 36, normalized size = 1. \[ -\frac{1}{2 x^2}+\frac{8}{3 x^3}-\frac{11}{2 x^4}+\frac{24}{5 x^5}-\frac{3}{2 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 27, normalized size = 0.8 \begin{align*} -{\frac{3}{2\,{x}^{6}}}+{\frac{24}{5\,{x}^{5}}}-{\frac{11}{2\,{x}^{4}}}+{\frac{8}{3\,{x}^{3}}}-{\frac{1}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00922, size = 34, normalized size = 0.94 \begin{align*} -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90917, size = 70, normalized size = 1.94 \begin{align*} -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116787, size = 26, normalized size = 0.72 \begin{align*} - \frac{15 x^{4} - 80 x^{3} + 165 x^{2} - 144 x + 45}{30 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10473, size = 34, normalized size = 0.94 \begin{align*} -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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