Optimal. Leaf size=19 \[ -2+\left (\frac {1}{5}+e^4\right ) x-\log \left ((-1+x)^4\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.11, 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 = {192, 45}
\begin {gather*} \frac {1}{5} \left (1+5 e^4\right ) x-4 \log (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 192
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-21-5 e^4+\left (1+5 e^4\right ) x}{-5+5 x} \, dx\\ &=\int \left (\frac {1}{5} \left (1+5 e^4\right )-\frac {4}{-1+x}\right ) \, dx\\ &=\frac {1}{5} \left (1+5 e^4\right ) x-4 \log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 1.16 \begin {gather*} \frac {1}{5} \left (\left (1+5 e^4\right ) (-1+x)-20 \log (-1+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.92, size = 15, normalized size = 0.79
method | result | size |
default | \(x \,{\mathrm e}^{4}+\frac {x}{5}-4 \ln \left (x -1\right )\) | \(15\) |
risch | \(x \,{\mathrm e}^{4}+\frac {x}{5}-4 \ln \left (x -1\right )\) | \(15\) |
norman | \(x \left (\frac {1}{5}+{\mathrm e}^{4}\right )-4 \ln \left (5 x -5\right )\) | \(16\) |
meijerg | \(-\frac {21 \ln \left (1-x \right )}{5}-\left (\frac {1}{5}+{\mathrm e}^{4}\right ) \left (-x -\ln \left (1-x \right )\right )-{\mathrm e}^{4} \ln \left (1-x \right )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 16, normalized size = 0.84 \begin {gather*} \frac {1}{5} \, x {\left (5 \, e^{4} + 1\right )} - 4 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 14, normalized size = 0.74 \begin {gather*} x e^{4} + \frac {1}{5} \, x - 4 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 14, normalized size = 0.74 \begin {gather*} x \left (\frac {1}{5} + e^{4}\right ) - 4 \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 15, normalized size = 0.79 \begin {gather*} x e^{4} + \frac {1}{5} \, x - 4 \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 0.68 \begin {gather*} x\,\left ({\mathrm {e}}^4+\frac {1}{5}\right )-4\,\ln \left (x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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