Optimal. Leaf size=42 \[ \frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2) \]
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Rubi [A] time = 0.0426682, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {1594, 1628} \[ \frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2) \]
Antiderivative was successfully verified.
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Rule 1594
Rule 1628
Rubi steps
\begin{align*} \int \frac{1+x^5}{-10 x-3 x^2+x^3} \, dx &=\int \frac{1+x^5}{x \left (-10-3 x+x^2\right )} \, dx\\ &=\int \left (19+\frac{3126}{35 (-5+x)}-\frac{1}{10 x}+3 x+x^2-\frac{31}{14 (2+x)}\right ) \, dx\\ &=19 x+\frac{3 x^2}{2}+\frac{x^3}{3}+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0067155, size = 42, normalized size = 1. \[ \frac{x^3}{3}+\frac{3 x^2}{2}+19 x+\frac{3126}{35} \log (5-x)-\frac{\log (x)}{10}-\frac{31}{14} \log (x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 31, normalized size = 0.7 \begin{align*}{\frac{{x}^{3}}{3}}+{\frac{3\,{x}^{2}}{2}}+19\,x-{\frac{31\,\ln \left ( 2+x \right ) }{14}}-{\frac{\ln \left ( x \right ) }{10}}+{\frac{3126\,\ln \left ( -5+x \right ) }{35}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970599, size = 41, normalized size = 0.98 \begin{align*} \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} + 19 \, x - \frac{31}{14} \, \log \left (x + 2\right ) + \frac{3126}{35} \, \log \left (x - 5\right ) - \frac{1}{10} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70858, size = 108, normalized size = 2.57 \begin{align*} \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} + 19 \, x - \frac{31}{14} \, \log \left (x + 2\right ) + \frac{3126}{35} \, \log \left (x - 5\right ) - \frac{1}{10} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.129621, size = 36, normalized size = 0.86 \begin{align*} \frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 19 x - \frac{\log{\left (x \right )}}{10} + \frac{3126 \log{\left (x - 5 \right )}}{35} - \frac{31 \log{\left (x + 2 \right )}}{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06358, size = 45, normalized size = 1.07 \begin{align*} \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} + 19 \, x - \frac{31}{14} \, \log \left ({\left | x + 2 \right |}\right ) + \frac{3126}{35} \, \log \left ({\left | x - 5 \right |}\right ) - \frac{1}{10} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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