Optimal. Leaf size=37 \[ -\frac {8}{(1-x)^2}+\frac {32}{1-x}+7 x+\frac {x^2}{2}+24 \log (1-x) \]
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Rubi [A]
time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2099}
\begin {gather*} \frac {x^2}{2}+7 x+\frac {32}{1-x}-\frac {8}{(1-x)^2}+24 \log (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (7+\frac {16}{(-1+x)^3}+\frac {32}{(-1+x)^2}+\frac {24}{-1+x}+x\right ) \, dx\\ &=-\frac {8}{(1-x)^2}+\frac {32}{1-x}+7 x+\frac {x^2}{2}+24 \log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 35, normalized size = 0.95 \begin {gather*} -\frac {8}{(-1+x)^2}-\frac {32}{-1+x}+8 (-1+x)+\frac {1}{2} (-1+x)^2+24 \log (-1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 30, normalized size = 0.81
method | result | size |
norman | \(\frac {-52 x +6 x^{3}+\frac {1}{2} x^{4}+\frac {75}{2}}{\left (x -1\right )^{2}}+24 \ln \left (x -1\right )\) | \(29\) |
default | \(\frac {x^{2}}{2}+7 x -\frac {32}{x -1}-\frac {8}{\left (x -1\right )^{2}}+24 \ln \left (x -1\right )\) | \(30\) |
risch | \(\frac {x^{2}}{2}+7 x +\frac {-32 x +24}{x^{2}-2 x +1}+24 \ln \left (x -1\right )\) | \(32\) |
parallelrisch | \(\frac {x^{4}+48 \ln \left (x -1\right ) x^{2}+12 x^{3}+75-96 \ln \left (x -1\right ) x +48 \ln \left (x -1\right )-104 x}{2 x^{2}-4 x +2}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.40, size = 32, normalized size = 0.86 \begin {gather*} \frac {1}{2} \, x^{2} + 7 \, x - \frac {8 \, {\left (4 \, x - 3\right )}}{x^{2} - 2 \, x + 1} + 24 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 44, normalized size = 1.19 \begin {gather*} \frac {x^{4} + 12 \, x^{3} - 27 \, x^{2} + 48 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (x - 1\right ) - 50 \, x + 48}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \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 = 0.73 \begin {gather*} \frac {x^{2}}{2} + 7 x + \frac {24 - 32 x}{x^{2} - 2 x + 1} + 24 \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 28, normalized size = 0.76 \begin {gather*} \frac {1}{2} \, x^{2} + 7 \, x - \frac {8 \, {\left (4 \, x - 3\right )}}{{\left (x - 1\right )}^{2}} + 24 \, \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 = 0.09, size = 32, normalized size = 0.86 \begin {gather*} 7\,x+24\,\ln \left (x-1\right )-\frac {32\,x-24}{x^2-2\,x+1}+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 22, normalized size = 0.59 \begin {gather*} \frac {3 \ln \left (x -1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\arctan \left (x \right )}{2}-\frac {x}{2} \end {gather*}
Warning: Unable to verify antiderivative.
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