Optimal. Leaf size=32 \[ \frac {x}{-x+\frac {\log \left (x \left (-3+\frac {2 (15+x) \left (e^3+x\right )}{x}\right )\right )}{-5+x}} \]
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Rubi [A]
time = 0.55, antiderivative size = 29, normalized size of antiderivative = 0.91, number of steps
used = 3, number of rules used = 3, integrand size = 218, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6820, 6843,
32} \begin {gather*} \frac {1}{1-\frac {(x-5) x}{\log \left (2 e^3 (x+15)+x (2 x+27)\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 6820
Rule 6843
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (135-2 e^3 (-5+x)-7 x-4 x^2\right )+(-5+2 x) \left (2 e^3 (15+x)+x (27+2 x)\right ) \log \left (2 e^3 (15+x)+x (27+2 x)\right )}{\left (30 e^3+\left (27+2 e^3\right ) x+2 x^2\right ) \left ((-5+x) x-\log \left (2 e^3 (15+x)+x (27+2 x)\right )\right )^2} \, dx\\ &=\text {Subst}\left (\int \frac {1}{(-1+x)^2} \, dx,x,\frac {(-5+x) x}{\log \left (2 e^3 (15+x)+x (27+2 x)\right )}\right )\\ &=\frac {1}{1-\frac {(-5+x) x}{\log \left (2 e^3 (15+x)+x (27+2 x)\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 33, normalized size = 1.03 \begin {gather*} \frac {(-5+x) x}{5 x-x^2+\log \left (2 e^3 (15+x)+x (27+2 x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.06, size = 36, normalized size = 1.12
method | result | size |
risch | \(-\frac {\left (x -5\right ) x}{x^{2}-5 x -\ln \left (\left (2 x +30\right ) {\mathrm e}^{3}+2 x^{2}+27 x \right )}\) | \(36\) |
norman | \(-\frac {\ln \left (\left (2 x +30\right ) {\mathrm e}^{3}+2 x^{2}+27 x \right )}{x^{2}-5 x -\ln \left (\left (2 x +30\right ) {\mathrm e}^{3}+2 x^{2}+27 x \right )}\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 39, normalized size = 1.22 \begin {gather*} -\frac {x^{2} - 5 \, x}{x^{2} - 5 \, x - \log \left (2 \, x^{2} + x {\left (2 \, e^{3} + 27\right )} + 30 \, e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 37, normalized size = 1.16 \begin {gather*} -\frac {x^{2} - 5 \, x}{x^{2} - 5 \, x - \log \left (2 \, x^{2} + 2 \, {\left (x + 15\right )} e^{3} + 27 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 31, normalized size = 0.97 \begin {gather*} \frac {x^{2} - 5 x}{- x^{2} + 5 x + \log {\left (2 x^{2} + 27 x + \left (2 x + 30\right ) e^{3} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {135\,x+\ln \left (27\,x+2\,x^2+{\mathrm {e}}^3\,\left (2\,x+30\right )\right )\,\left ({\mathrm {e}}^3\,\left (4\,x^2+50\,x-150\right )-135\,x+44\,x^2+4\,x^3\right )+{\mathrm {e}}^3\,\left (10\,x-2\,x^2\right )-7\,x^2-4\,x^3}{675\,x^3-\ln \left (27\,x+2\,x^2+{\mathrm {e}}^3\,\left (2\,x+30\right )\right )\,\left ({\mathrm {e}}^3\,\left (4\,x^3+40\,x^2-300\,x\right )-270\,x^2+34\,x^3+4\,x^4\right )-220\,x^4+7\,x^5+2\,x^6+{\ln \left (27\,x+2\,x^2+{\mathrm {e}}^3\,\left (2\,x+30\right )\right )}^2\,\left (27\,x+2\,x^2+{\mathrm {e}}^3\,\left (2\,x+30\right )\right )+{\mathrm {e}}^3\,\left (2\,x^5+10\,x^4-250\,x^3+750\,x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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