Optimal. Leaf size=25 \[ -\frac {3 (-1+x) (1+x)}{2 \sqrt [3]{(-1+x)^4 (1+x)^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, 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 = {6851, 37}
\begin {gather*} \frac {3 (1-x) (x+1)}{2 \sqrt [3]{(1-x)^4 (x+1)^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 6851
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 = 0.02, size = 25, normalized size = 1.00 \begin {gather*} -\frac {3 (-1+x) (1+x)}{2 \sqrt [3]{(-1+x)^4 (1+x)^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 22, normalized size = 0.88
method | result | size |
gosper | \(-\frac {3 \left (-1+x \right ) \left (1+x \right )}{2 \left (\left (-1+x \right )^{4} \left (1+x \right )^{2}\right )^{\frac {1}{3}}}\) | \(22\) |
risch | \(-\frac {3 \left (-1+x \right ) \left (1+x \right )}{2 \left (\left (-1+x \right )^{4} \left (1+x \right )^{2}\right )^{\frac {1}{3}}}\) | \(22\) |
trager | \(-\frac {3 \left (x^{6}-2 x^{5}-x^{4}+4 x^{3}-x^{2}-2 x +1\right )^{\frac {2}{3}}}{2 \left (1+x \right ) \left (-1+x \right )^{3}}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 47 vs.
\(2 (21) = 42\).
time = 0.38, size = 47, normalized size = 1.88 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt [3]{\left (x - 1\right )^{4} \left (x + 1\right )^{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.24, size = 25, normalized size = 1.00 \begin {gather*} -\frac {3\,{\left ({\left (x-1\right )}^4\,{\left (x+1\right )}^2\right )}^{2/3}}{2\,{\left (x-1\right )}^3\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________