Optimal. Leaf size=42 \[ 19 x+\frac {3 x^2}{2}+\frac {x^3}{3}+\frac {3126}{35} \log (5-x)-\frac {\log (x)}{10}-\frac {31}{14} \log (2+x) \]
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Rubi [A]
time = 0.03, antiderivative size = 42, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1608, 1642}
\begin {gather*} \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) \end {gather*}
Antiderivative was successfully verified.
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Rule 1608
Rule 1642
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*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 1.00 \begin {gather*} 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 {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 31, normalized size = 0.74
method | result | size |
default | \(\frac {x^{3}}{3}+\frac {3 x^{2}}{2}+19 x -\frac {31 \ln \left (x +2\right )}{14}+\frac {3126 \ln \left (-5+x \right )}{35}-\frac {\ln \left (x \right )}{10}\) | \(31\) |
norman | \(\frac {x^{3}}{3}+\frac {3 x^{2}}{2}+19 x -\frac {31 \ln \left (x +2\right )}{14}+\frac {3126 \ln \left (-5+x \right )}{35}-\frac {\ln \left (x \right )}{10}\) | \(31\) |
risch | \(\frac {x^{3}}{3}+\frac {3 x^{2}}{2}+19 x -\frac {31 \ln \left (x +2\right )}{14}+\frac {3126 \ln \left (-5+x \right )}{35}-\frac {\ln \left (x \right )}{10}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 30, normalized size = 0.71 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 30, normalized size = 0.71 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 36, normalized size = 0.86 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.42, size = 33, normalized size = 0.79 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 30, normalized size = 0.71 \begin {gather*} 19\,x-\frac {31\,\ln \left (x+2\right )}{14}+\frac {3126\,\ln \left (x-5\right )}{35}-\frac {\ln \left (x\right )}{10}+\frac {3\,x^2}{2}+\frac {x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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