Optimal. Leaf size=27 \[ \left (2-e^{16}-\frac {2}{x}+4 x\right )^2 \left (x-x^2\right )^2 \]
________________________________________________________________________________________
Rubi [B] time = 0.05, antiderivative size = 89, normalized size of antiderivative = 3.30, number of steps used = 3, number of rules used = 0, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^6-8 e^{16} x^5-16 x^5+e^{32} x^4+12 e^{16} x^4-28 x^4-2 e^{32} x^3+4 e^{16} x^3+32 x^3+e^{32} x^2-12 e^{16} x^2+8 x^2+4 e^{16} x-16 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-16 x+8 x^2+32 x^3-28 x^4-16 x^5+16 x^6+e^{16} \int \left (4-24 x+12 x^2+48 x^3-40 x^4\right ) \, dx+e^{32} \int \left (2 x-6 x^2+4 x^3\right ) \, dx\\ &=-16 x+4 e^{16} x+8 x^2-12 e^{16} x^2+e^{32} x^2+32 x^3+4 e^{16} x^3-2 e^{32} x^3-28 x^4+12 e^{16} x^4+e^{32} x^4-16 x^5-8 e^{16} x^5+16 x^6\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.01, size = 89, normalized size = 3.30 \begin {gather*} -16 x+4 e^{16} x+8 x^2-12 e^{16} x^2+e^{32} x^2+32 x^3+4 e^{16} x^3-2 e^{32} x^3-28 x^4+12 e^{16} x^4+e^{32} x^4-16 x^5-8 e^{16} x^5+16 x^6 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.83, size = 72, normalized size = 2.67 \begin {gather*} 16 \, x^{6} - 16 \, x^{5} - 28 \, x^{4} + 32 \, x^{3} + 8 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{32} - 4 \, {\left (2 \, x^{5} - 3 \, x^{4} - x^{3} + 3 \, x^{2} - x\right )} e^{16} - 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.33, size = 72, normalized size = 2.67 \begin {gather*} 16 \, x^{6} - 16 \, x^{5} - 28 \, x^{4} + 32 \, x^{3} + 8 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{32} - 4 \, {\left (2 \, x^{5} - 3 \, x^{4} - x^{3} + 3 \, x^{2} - x\right )} e^{16} - 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.03, size = 69, normalized size = 2.56
method | result | size |
norman | \(\left (-8 \,{\mathrm e}^{16}-16\right ) x^{5}+\left (4 \,{\mathrm e}^{16}-16\right ) x +\left (-2 \,{\mathrm e}^{32}+4 \,{\mathrm e}^{16}+32\right ) x^{3}+\left ({\mathrm e}^{32}-12 \,{\mathrm e}^{16}+8\right ) x^{2}+\left ({\mathrm e}^{32}+12 \,{\mathrm e}^{16}-28\right ) x^{4}+16 x^{6}\) | \(69\) |
default | \({\mathrm e}^{32} \left (x^{4}-2 x^{3}+x^{2}\right )+{\mathrm e}^{16} \left (-8 x^{5}+12 x^{4}+4 x^{3}-12 x^{2}+4 x \right )+16 x^{6}-16 x^{5}-28 x^{4}+32 x^{3}+8 x^{2}-16 x\) | \(74\) |
gosper | \(x \left ({\mathrm e}^{32} x^{3}-8 \,{\mathrm e}^{16} x^{4}+16 x^{5}-2 \,{\mathrm e}^{32} x^{2}+12 x^{3} {\mathrm e}^{16}-16 x^{4}+x \,{\mathrm e}^{32}+4 x^{2} {\mathrm e}^{16}-28 x^{3}-12 x \,{\mathrm e}^{16}+32 x^{2}+4 \,{\mathrm e}^{16}+8 x -16\right )\) | \(81\) |
risch | \(x^{4} {\mathrm e}^{32}-2 \,{\mathrm e}^{32} x^{3}+{\mathrm e}^{32} x^{2}-8 \,{\mathrm e}^{16} x^{5}+12 \,{\mathrm e}^{16} x^{4}+4 x^{3} {\mathrm e}^{16}-12 x^{2} {\mathrm e}^{16}+4 x \,{\mathrm e}^{16}+16 x^{6}-16 x^{5}-28 x^{4}+32 x^{3}+8 x^{2}-16 x\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.39, size = 72, normalized size = 2.67 \begin {gather*} 16 \, x^{6} - 16 \, x^{5} - 28 \, x^{4} + 32 \, x^{3} + 8 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{32} - 4 \, {\left (2 \, x^{5} - 3 \, x^{4} - x^{3} + 3 \, x^{2} - x\right )} e^{16} - 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 63, normalized size = 2.33 \begin {gather*} 16\,x^6+\left (-8\,{\mathrm {e}}^{16}-16\right )\,x^5+\left (12\,{\mathrm {e}}^{16}+{\mathrm {e}}^{32}-28\right )\,x^4+\left (4\,{\mathrm {e}}^{16}-2\,{\mathrm {e}}^{32}+32\right )\,x^3+\left ({\mathrm {e}}^{32}-12\,{\mathrm {e}}^{16}+8\right )\,x^2+\left (4\,{\mathrm {e}}^{16}-16\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.07, size = 66, normalized size = 2.44 \begin {gather*} 16 x^{6} + x^{5} \left (- 8 e^{16} - 16\right ) + x^{4} \left (-28 + 12 e^{16} + e^{32}\right ) + x^{3} \left (- 2 e^{32} + 32 + 4 e^{16}\right ) + x^{2} \left (- 12 e^{16} + 8 + e^{32}\right ) + x \left (-16 + 4 e^{16}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________