Optimal. Leaf size=26 \[ \left (x^2+\frac {4 x^4}{3}\right ) \left (-3+\frac {x}{\left (x-\frac {x}{e^5}\right )^2}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(130\) vs. \(2(26)=52\).
time = 0.02, antiderivative size = 130, normalized size of antiderivative = 5.00, number of steps
used = 4, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {12}
\begin {gather*} -\frac {4 e^{10} x^4}{\left (1-e^5\right )^2}+\frac {8 e^5 x^4}{\left (1-e^5\right )^2}-\frac {4 x^4}{\left (1-e^5\right )^2}+\frac {4 e^{10} x^3}{3 \left (1-e^5\right )^2}-\frac {3 e^{10} x^2}{\left (1-e^5\right )^2}+\frac {6 e^5 x^2}{\left (1-e^5\right )^2}-\frac {3 x^2}{\left (1-e^5\right )^2}+\frac {e^{10} x}{\left (1-e^5\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-6 x-16 x^3+e^{10} \left (1-6 x+4 x^2-16 x^3\right )+e^5 \left (12 x+32 x^3\right )\right ) \, dx}{1-2 e^5+e^{10}}\\ &=-\frac {3 x^2}{\left (1-e^5\right )^2}-\frac {4 x^4}{\left (1-e^5\right )^2}+\frac {e^5 \int \left (12 x+32 x^3\right ) \, dx}{\left (1-e^5\right )^2}+\frac {e^{10} \int \left (1-6 x+4 x^2-16 x^3\right ) \, dx}{\left (1-e^5\right )^2}\\ &=\frac {e^{10} x}{\left (1-e^5\right )^2}-\frac {3 x^2}{\left (1-e^5\right )^2}+\frac {6 e^5 x^2}{\left (1-e^5\right )^2}-\frac {3 e^{10} x^2}{\left (1-e^5\right )^2}+\frac {4 e^{10} x^3}{3 \left (1-e^5\right )^2}-\frac {4 x^4}{\left (1-e^5\right )^2}+\frac {8 e^5 x^4}{\left (1-e^5\right )^2}-\frac {4 e^{10} x^4}{\left (1-e^5\right )^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(66\) vs. \(2(26)=52\).
time = 0.01, size = 66, normalized size = 2.54 \begin {gather*} \frac {e^{10} x-3 x^2+6 e^5 x^2-3 e^{10} x^2+\frac {4 e^{10} x^3}{3}-4 x^4+8 e^5 x^4-4 e^{10} x^4}{\left (-1+e^5\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs.
\(2(25)=50\).
time = 0.33, size = 72, normalized size = 2.77
method | result | size |
norman | \(\frac {\left (3-3 \,{\mathrm e}^{5}\right ) x^{2}+\left (-4 \,{\mathrm e}^{5}+4\right ) x^{4}+\frac {{\mathrm e}^{10} x}{{\mathrm e}^{5}-1}+\frac {4 \,{\mathrm e}^{10} x^{3}}{3 \left ({\mathrm e}^{5}-1\right )}}{{\mathrm e}^{5}-1}\) | \(56\) |
gosper | \(-\frac {x \left (12 x^{3} {\mathrm e}^{10}-4 \,{\mathrm e}^{10} x^{2}-24 x^{3} {\mathrm e}^{5}+9 x \,{\mathrm e}^{10}+12 x^{3}-3 \,{\mathrm e}^{10}-18 x \,{\mathrm e}^{5}+9 x \right )}{3 \left ({\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1\right )}\) | \(68\) |
default | \(\frac {-4 x^{4} {\mathrm e}^{10}+\frac {4 x^{3} {\mathrm e}^{10}}{3}+8 x^{4} {\mathrm e}^{5}-3 \,{\mathrm e}^{10} x^{2}-4 x^{4}+x \,{\mathrm e}^{10}+6 x^{2} {\mathrm e}^{5}-3 x^{2}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}\) | \(72\) |
risch | \(-\frac {4 x^{4} {\mathrm e}^{10}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}+\frac {4 x^{3} {\mathrm e}^{10}}{3 \left ({\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1\right )}+\frac {8 x^{4} {\mathrm e}^{5}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}-\frac {3 x^{2} {\mathrm e}^{10}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}-\frac {4 x^{4}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}+\frac {x \,{\mathrm e}^{10}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}+\frac {6 x^{2} {\mathrm e}^{5}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}-\frac {3 x^{2}}{{\mathrm e}^{10}-2 \,{\mathrm e}^{5}+1}\) | \(131\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs.
\(2 (27) = 54\).
time = 0.30, size = 60, normalized size = 2.31 \begin {gather*} -\frac {12 \, x^{4} + 9 \, x^{2} + {\left (12 \, x^{4} - 4 \, x^{3} + 9 \, x^{2} - 3 \, x\right )} e^{10} - 6 \, {\left (4 \, x^{4} + 3 \, x^{2}\right )} e^{5}}{3 \, {\left (e^{10} - 2 \, e^{5} + 1\right )}} \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. 60 vs.
\(2 (27) = 54\).
time = 0.36, size = 60, normalized size = 2.31 \begin {gather*} -\frac {12 \, x^{4} + 9 \, x^{2} + {\left (12 \, x^{4} - 4 \, x^{3} + 9 \, x^{2} - 3 \, x\right )} e^{10} - 6 \, {\left (4 \, x^{4} + 3 \, x^{2}\right )} e^{5}}{3 \, {\left (e^{10} - 2 \, e^{5} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (20) = 40\).
time = 0.02, size = 44, normalized size = 1.69 \begin {gather*} - 4 x^{4} + \frac {4 x^{3} e^{10}}{- 6 e^{5} + 3 + 3 e^{10}} - 3 x^{2} + \frac {x e^{10}}{- 2 e^{5} + 1 + e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs.
\(2 (27) = 54\).
time = 0.41, size = 60, normalized size = 2.31 \begin {gather*} -\frac {12 \, x^{4} + 9 \, x^{2} + {\left (12 \, x^{4} - 4 \, x^{3} + 9 \, x^{2} - 3 \, x\right )} e^{10} - 6 \, {\left (4 \, x^{4} + 3 \, x^{2}\right )} e^{5}}{3 \, {\left (e^{10} - 2 \, e^{5} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.10, size = 34, normalized size = 1.31 \begin {gather*} -4\,x^4+\frac {4\,{\mathrm {e}}^{10}\,x^3}{3\,{\left ({\mathrm {e}}^5-1\right )}^2}-3\,x^2+\frac {{\mathrm {e}}^{10}\,x}{{\left ({\mathrm {e}}^5-1\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________