Optimal. Leaf size=26 \[ 4 \left (7+\frac {e^4}{2 x}+x+2 \left (5-x^2\right )^4\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.23, number of steps used = 2, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {14} \begin {gather*} 8 x^8-160 x^6+1200 x^4-4000 x^2+4 x+\frac {2 e^4}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4-\frac {2 e^4}{x^2}-8000 x+4800 x^3-960 x^5+64 x^7\right ) \, dx\\ &=\frac {2 e^4}{x}+4 x-4000 x^2+1200 x^4-160 x^6+8 x^8\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 32, normalized size = 1.23 \begin {gather*} \frac {2 e^4}{x}+4 x-4000 x^2+1200 x^4-160 x^6+8 x^8 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.02, size = 33, normalized size = 1.27 \begin {gather*} \frac {2 \, {\left (4 \, x^{9} - 80 \, x^{7} + 600 \, x^{5} - 2000 \, x^{3} + 2 \, x^{2} + e^{4}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.28, size = 31, normalized size = 1.19 \begin {gather*} 8 \, x^{8} - 160 \, x^{6} + 1200 \, x^{4} - 4000 \, x^{2} + 4 \, x + \frac {2 \, e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 32, normalized size = 1.23
method | result | size |
default | \(8 x^{8}-160 x^{6}+1200 x^{4}-4000 x^{2}+4 x +\frac {2 \,{\mathrm e}^{4}}{x}\) | \(32\) |
risch | \(8 x^{8}-160 x^{6}+1200 x^{4}-4000 x^{2}+4 x +\frac {2 \,{\mathrm e}^{4}}{x}\) | \(32\) |
gosper | \(\frac {4 x^{2}-4000 x^{3}+1200 x^{5}-160 x^{7}+8 x^{9}+2 \,{\mathrm e}^{4}}{x}\) | \(34\) |
norman | \(\frac {4 x^{2}-4000 x^{3}+1200 x^{5}-160 x^{7}+8 x^{9}+2 \,{\mathrm e}^{4}}{x}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.69, size = 31, normalized size = 1.19 \begin {gather*} 8 \, x^{8} - 160 \, x^{6} + 1200 \, x^{4} - 4000 \, x^{2} + 4 \, x + \frac {2 \, e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 31, normalized size = 1.19 \begin {gather*} 4\,x+\frac {2\,{\mathrm {e}}^4}{x}-4000\,x^2+1200\,x^4-160\,x^6+8\,x^8 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 29, normalized size = 1.12 \begin {gather*} 8 x^{8} - 160 x^{6} + 1200 x^{4} - 4000 x^{2} + 4 x + \frac {2 e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________