Optimal. Leaf size=36 \[ \frac{6}{1-x}-\frac{6}{(1-x)^2}+\frac{8}{3 (1-x)^3}+\log (1-x) \]
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Rubi [A] time = 0.0130342, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{6}{1-x}-\frac{6}{(1-x)^2}+\frac{8}{3 (1-x)^3}+\log (1-x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(1+x)^3}{(-1+x)^4} \, dx &=\int \left (\frac{8}{(-1+x)^4}+\frac{12}{(-1+x)^3}+\frac{6}{(-1+x)^2}+\frac{1}{-1+x}\right ) \, dx\\ &=\frac{8}{3 (1-x)^3}-\frac{6}{(1-x)^2}+\frac{6}{1-x}+\log (1-x)\\ \end{align*}
Mathematica [A] time = 0.0113566, size = 24, normalized size = 0.67 \[ \log (x-1)-\frac{2 \left (9 x^2-9 x+4\right )}{3 (x-1)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{8}{3\, \left ( -1+x \right ) ^{3}}}-6\, \left ( -1+x \right ) ^{-2}+\ln \left ( -1+x \right ) -6\, \left ( -1+x \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.948822, size = 43, normalized size = 1.19 \begin{align*} -\frac{2 \,{\left (9 \, x^{2} - 9 \, x + 4\right )}}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84015, size = 120, normalized size = 3.33 \begin{align*} -\frac{18 \, x^{2} - 3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )} \log \left (x - 1\right ) - 18 \, x + 8}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.109386, size = 29, normalized size = 0.81 \begin{align*} - \frac{18 x^{2} - 18 x + 8}{3 x^{3} - 9 x^{2} + 9 x - 3} + \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06742, size = 31, normalized size = 0.86 \begin{align*} -\frac{2 \,{\left (9 \, x^{2} - 9 \, x + 4\right )}}{3 \,{\left (x - 1\right )}^{3}} + \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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