Optimal. Leaf size=25 \[ -\frac{3 (x-1) (x+1)}{2 \sqrt [3]{(x-1)^4 (x+1)^2}} \]
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Rubi [A] time = 0.0128641, antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {6719, 37} \[ \frac{3 (1-x) (x+1)}{2 \sqrt [3]{(1-x)^4 (x+1)^2}} \]
Antiderivative was successfully verified.
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Rule 6719
Rule 37
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{(-1+x)^4 (1+x)^2}} \, dx &=\frac{\left ((-1+x)^{4/3} (1+x)^{2/3}\right ) \int \frac{1}{(-1+x)^{4/3} (1+x)^{2/3}} \, dx}{\sqrt [3]{(-1+x)^4 (1+x)^2}}\\ &=\frac{3 (1-x) (1+x)}{2 \sqrt [3]{(1-x)^4 (1+x)^2}}\\ \end{align*}
Mathematica [A] time = 0.0078621, size = 25, normalized size = 1. \[ -\frac{3 (x-1) (x+1)}{2 \sqrt [3]{(x-1)^4 (x+1)^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 22, normalized size = 0.9 \begin{align*} -{\frac{ \left ( -3+3\,x \right ) \left ( 1+x \right ) }{2}{\frac{1}{\sqrt [3]{ \left ( -1+x \right ) ^{4} \left ( 1+x \right ) ^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left ({\left (x + 1\right )}^{2}{\left (x - 1\right )}^{4}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.77818, size = 108, normalized size = 4.32 \begin{align*} -\frac{3 \,{\left (x^{6} - 2 \, x^{5} - x^{4} + 4 \, x^{3} - x^{2} - 2 \, x + 1\right )}^{\frac{2}{3}}}{2 \,{\left (x^{4} - 2 \, x^{3} + 2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt [3]{\left (x - 1\right )^{4} \left (x + 1\right )^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left ({\left (x + 1\right )}^{2}{\left (x - 1\right )}^{4}\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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