Optimal. Leaf size=23 \[ \frac {16 e^8 \left (-3+\frac {-1+2 x}{x}\right )^2}{9 x^4} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.35, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14} \begin {gather*} \frac {16 e^8}{9 x^6}+\frac {32 e^8}{9 x^5}+\frac {16 e^8}{9 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} e^8 \int \frac {-96-160 x-64 x^2}{x^7} \, dx\\ &=\frac {1}{9} e^8 \int \left (-\frac {96}{x^7}-\frac {160}{x^6}-\frac {64}{x^5}\right ) \, dx\\ &=\frac {16 e^8}{9 x^6}+\frac {32 e^8}{9 x^5}+\frac {16 e^8}{9 x^4}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 27, normalized size = 1.17 \begin {gather*} -\frac {32}{9} e^8 \left (-\frac {1}{2 x^6}-\frac {1}{x^5}-\frac {1}{2 x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.69, size = 15, normalized size = 0.65 \begin {gather*} \frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 15, normalized size = 0.65 \begin {gather*} \frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 18, normalized size = 0.78
method | result | size |
gosper | \(\frac {16 \left (x^{2}+2 x +1\right ) {\mathrm e}^{8}}{9 x^{6}}\) | \(18\) |
risch | \(\frac {{\mathrm e}^{8} \left (16 x^{2}+32 x +16\right )}{9 x^{6}}\) | \(18\) |
default | \(\frac {32 \,{\mathrm e}^{8} \left (\frac {1}{x^{5}}+\frac {1}{2 x^{6}}+\frac {1}{2 x^{4}}\right )}{9}\) | \(21\) |
norman | \(\frac {\frac {16 \,{\mathrm e}^{8}}{9}+\frac {32 x \,{\mathrm e}^{8}}{9}+\frac {16 x^{2} {\mathrm e}^{8}}{9}}{x^{6}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 15, normalized size = 0.65 \begin {gather*} \frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 22, normalized size = 0.96 \begin {gather*} \frac {16\,{\mathrm {e}}^8\,x^2+32\,{\mathrm {e}}^8\,x+16\,{\mathrm {e}}^8}{9\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 27, normalized size = 1.17 \begin {gather*} - \frac {- 16 x^{2} e^{8} - 32 x e^{8} - 16 e^{8}}{9 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________