Optimal. Leaf size=27 \[ \frac {(5+x) \left (x-4 e^3 \left (\frac {x}{4}+x^2\right )-\log (5)\right )}{x} \]
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Rubi [A]
time = 0.07, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps
used = 4, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {1607, 1600, 14}
\begin {gather*} -4 e^3 x^2+\left (1-21 e^3\right ) x-\frac {5 \log (5)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 1600
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2+4 x^3+e^3 \left (-21 x-8 x^2\right ) \left (x+4 x^2\right )+(5+20 x) \log (5)}{x^2 (1+4 x)} \, dx\\ &=\int \frac {\left (1-21 e^3\right ) x^2-8 e^3 x^3+5 \log (5)}{x^2} \, dx\\ &=\int \left (1-21 e^3-8 e^3 x+\frac {5 \log (5)}{x^2}\right ) \, dx\\ &=\left (1-21 e^3\right ) x-4 e^3 x^2-\frac {5 \log (5)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 23, normalized size = 0.85 \begin {gather*} x-21 e^3 x-4 e^3 x^2-\frac {5 \log (5)}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.00, size = 23, normalized size = 0.85
method | result | size |
risch | \(-4 x^{2} {\mathrm e}^{3}-21 x \,{\mathrm e}^{3}+x -\frac {5 \ln \left (5\right )}{x}\) | \(22\) |
default | \(x -\frac {5 \ln \left (5\right )}{x}-{\mathrm e}^{3} \left (4 x^{2}+21 x \right )\) | \(23\) |
norman | \(\frac {\left (-21 \,{\mathrm e}^{3}+1\right ) x^{2}-4 x^{3} {\mathrm e}^{3}-5 \ln \left (5\right )}{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 24, normalized size = 0.89 \begin {gather*} -4 \, x^{2} e^{3} - x {\left (21 \, e^{3} - 1\right )} - \frac {5 \, \log \left (5\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 27, normalized size = 1.00 \begin {gather*} \frac {x^{2} - {\left (4 \, x^{3} + 21 \, x^{2}\right )} e^{3} - 5 \, \log \left (5\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 24, normalized size = 0.89 \begin {gather*} - 4 x^{2} e^{3} - x \left (-1 + 21 e^{3}\right ) - \frac {5 \log {\left (5 \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 0.78 \begin {gather*} -4 \, x^{2} e^{3} - 21 \, x e^{3} + x - \frac {5 \, \log \left (5\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 24, normalized size = 0.89 \begin {gather*} -4\,x^2\,{\mathrm {e}}^3-\frac {5\,\ln \left (5\right )}{x}-x\,\left (21\,{\mathrm {e}}^3-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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