Optimal. Leaf size=27 \[ -5+e^{2 e^5} \left (\frac {5}{x}-x\right )+x+5 x^2+\log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.22, number of steps
used = 2, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {14}
\begin {gather*} 5 x^2+\left (1-e^{2 e^5}\right ) x+\frac {5 e^{2 e^5}}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-e^{2 e^5}-\frac {5 e^{2 e^5}}{x^2}+\frac {1}{x}+10 x\right ) \, dx\\ &=\frac {5 e^{2 e^5}}{x}+\left (1-e^{2 e^5}\right ) x+5 x^2+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 27, normalized size = 1.00 \begin {gather*} e^{2 e^5} \left (\frac {5}{x}-x\right )+x (1+5 x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.35, size = 28, normalized size = 1.04
method | result | size |
default | \(5 x^{2}-{\mathrm e}^{2 \,{\mathrm e}^{5}} x +x +\frac {5 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}{x}+\ln \left (x \right )\) | \(28\) |
risch | \(5 x^{2}-{\mathrm e}^{2 \,{\mathrm e}^{5}} x +x +\frac {5 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}{x}+\ln \left (x \right )\) | \(28\) |
norman | \(\frac {\left (-{\mathrm e}^{2 \,{\mathrm e}^{5}}+1\right ) x^{2}+5 x^{3}+5 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}{x}+\ln \left (x \right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 28, normalized size = 1.04 \begin {gather*} 5 \, x^{2} - x {\left (e^{\left (2 \, e^{5}\right )} - 1\right )} + \frac {5 \, e^{\left (2 \, e^{5}\right )}}{x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 29, normalized size = 1.07 \begin {gather*} \frac {5 \, x^{3} + x^{2} - {\left (x^{2} - 5\right )} e^{\left (2 \, e^{5}\right )} + x \log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 27, normalized size = 1.00 \begin {gather*} 5 x^{2} + x \left (1 - e^{2 e^{5}}\right ) + \log {\left (x \right )} + \frac {5 e^{2 e^{5}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 28, normalized size = 1.04 \begin {gather*} 5 \, x^{2} - x e^{\left (2 \, e^{5}\right )} + x + \frac {5 \, e^{\left (2 \, e^{5}\right )}}{x} + \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 = 4.09, size = 28, normalized size = 1.04 \begin {gather*} \ln \left (x\right )-x\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^5}-1\right )+\frac {5\,{\mathrm {e}}^{2\,{\mathrm {e}}^5}}{x}+5\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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