Optimal. Leaf size=25 \[ \frac {4 (-1+x) (2+x)}{3 \sqrt [4]{(-1+x)^3 (2+x)^5}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.20, 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 {4 (1-x) (x+2)}{3 \sqrt [4]{-(1-x)^3 (x+2)^5}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 6851
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [4]{(-1+x)^3 (2+x)^5}} \, dx &=\frac {\left ((-1+x)^{3/4} (2+x)^{5/4}\right ) \int \frac {1}{(-1+x)^{3/4} (2+x)^{5/4}} \, dx}{\sqrt [4]{(-1+x)^3 (2+x)^5}}\\ &=-\frac {4 (1-x) (2+x)}{3 \sqrt [4]{-(1-x)^3 (2+x)^5}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 25, normalized size = 1.00 \begin {gather*} \frac {4 (-1+x) (2+x)}{3 \sqrt [4]{(-1+x)^3 (2+x)^5}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 22, normalized size = 0.88
method | result | size |
gosper | \(\frac {4 \left (-1+x \right ) \left (2+x \right )}{3 \left (\left (-1+x \right )^{3} \left (2+x \right )^{5}\right )^{\frac {1}{4}}}\) | \(22\) |
risch | \(\frac {4 \left (-1+x \right ) \left (2+x \right )}{3 \left (\left (-1+x \right )^{3} \left (2+x \right )^{5}\right )^{\frac {1}{4}}}\) | \(22\) |
trager | \(\frac {4 \left (x^{8}+7 x^{7}+13 x^{6}-11 x^{5}-50 x^{4}-8 x^{3}+64 x^{2}+16 x -32\right )^{\frac {3}{4}}}{3 \left (-1+x \right )^{2} \left (2+x \right )^{4}}\) | \(53\) |
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. 69 vs.
\(2 (21) = 42\).
time = 0.36, size = 69, normalized size = 2.76 \begin {gather*} \frac {4 \, {\left (x^{8} + 7 \, x^{7} + 13 \, x^{6} - 11 \, x^{5} - 50 \, x^{4} - 8 \, x^{3} + 64 \, x^{2} + 16 \, x - 32\right )}^{\frac {3}{4}}}{3 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4} - 8 \, x^{3} - 24 \, x^{2} + 16\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 [4]{\left (x - 1\right )^{3} \left (x + 2\right )^{5}}}\, 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 = 0.26, size = 25, normalized size = 1.00 \begin {gather*} \frac {4\,{\left ({\left (x-1\right )}^3\,{\left (x+2\right )}^5\right )}^{3/4}}{3\,{\left (x-1\right )}^2\,{\left (x+2\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________