Optimal. Leaf size=25 \[ -1+\frac {e^{2 x+\frac {x}{e^8 (5-x)}}}{x}+x \]
________________________________________________________________________________________
Rubi [F] time = 2.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^8 \left (25 x^2-10 x^3+x^4\right )+\exp \left (\frac {-x+e^8 \left (-10 x+2 x^2\right )}{e^8 (-5+x)}\right ) \left (5 x+e^8 \left (-25+60 x-21 x^2+2 x^3\right )\right )}{e^8 \left (25 x^2-10 x^3+x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^8 \left (25 x^2-10 x^3+x^4\right )+\exp \left (\frac {-x+e^8 \left (-10 x+2 x^2\right )}{e^8 (-5+x)}\right ) \left (5 x+e^8 \left (-25+60 x-21 x^2+2 x^3\right )\right )}{25 x^2-10 x^3+x^4} \, dx}{e^8}\\ &=\frac {\int \frac {e^8 \left (25 x^2-10 x^3+x^4\right )+\exp \left (\frac {-x+e^8 \left (-10 x+2 x^2\right )}{e^8 (-5+x)}\right ) \left (5 x+e^8 \left (-25+60 x-21 x^2+2 x^3\right )\right )}{x^2 \left (25-10 x+x^2\right )} \, dx}{e^8}\\ &=\frac {\int \frac {e^8 \left (25 x^2-10 x^3+x^4\right )+\exp \left (\frac {-x+e^8 \left (-10 x+2 x^2\right )}{e^8 (-5+x)}\right ) \left (5 x+e^8 \left (-25+60 x-21 x^2+2 x^3\right )\right )}{(-5+x)^2 x^2} \, dx}{e^8}\\ &=\frac {\int \left (e^8+\frac {e^{2 x-\frac {x}{e^8 (-5+x)}} \left (-25 e^8+5 \left (1+12 e^8\right ) x-21 e^8 x^2+2 e^8 x^3\right )}{(5-x)^2 x^2}\right ) \, dx}{e^8}\\ &=x+\frac {\int \frac {e^{2 x-\frac {x}{e^8 (-5+x)}} \left (-25 e^8+5 \left (1+12 e^8\right ) x-21 e^8 x^2+2 e^8 x^3\right )}{(5-x)^2 x^2} \, dx}{e^8}\\ &=x+\frac {\int \left (\frac {e^{2 x-\frac {x}{e^8 (-5+x)}}}{(-5+x)^2}-\frac {e^{2 x-\frac {x}{e^8 (-5+x)}}}{5 (-5+x)}-\frac {e^{8+2 x-\frac {x}{e^8 (-5+x)}}}{x^2}+\frac {e^{2 x-\frac {x}{e^8 (-5+x)}} \left (1+10 e^8\right )}{5 x}\right ) \, dx}{e^8}\\ &=x+\frac {1}{5} \left (10+\frac {1}{e^8}\right ) \int \frac {e^{2 x-\frac {x}{e^8 (-5+x)}}}{x} \, dx-\frac {\int \frac {e^{2 x-\frac {x}{e^8 (-5+x)}}}{-5+x} \, dx}{5 e^8}+\frac {\int \frac {e^{2 x-\frac {x}{e^8 (-5+x)}}}{(-5+x)^2} \, dx}{e^8}-\frac {\int \frac {e^{8+2 x-\frac {x}{e^8 (-5+x)}}}{x^2} \, dx}{e^8}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.42, size = 22, normalized size = 0.88 \begin {gather*} \frac {e^{\left (2-\frac {1}{e^8 (-5+x)}\right ) x}}{x}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.71, size = 32, normalized size = 1.28 \begin {gather*} \frac {x^{2} + e^{\left (\frac {{\left (2 \, {\left (x^{2} - 5 \, x\right )} e^{8} - x\right )} e^{\left (-8\right )}}{x - 5}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.38, size = 44, normalized size = 1.76 \begin {gather*} \frac {{\left (x^{2} e^{8} + e^{\left (\frac {2 \, x^{2} e^{8} - 10 \, x e^{8} - x}{x e^{8} - 5 \, e^{8}} + 8\right )}\right )} e^{\left (-8\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.23, size = 28, normalized size = 1.12
method | result | size |
risch | \(x +\frac {{\mathrm e}^{\frac {x \left (2 x \,{\mathrm e}^{8}-10 \,{\mathrm e}^{8}-1\right ) {\mathrm e}^{-8}}{x -5}}}{x}\) | \(28\) |
norman | \(\frac {\left (x^{3} {\mathrm e}^{4}-25 x \,{\mathrm e}^{4}+x \,{\mathrm e}^{4} {\mathrm e}^{\frac {\left (\left (2 x^{2}-10 x \right ) {\mathrm e}^{8}-x \right ) {\mathrm e}^{-8}}{x -5}}-5 \,{\mathrm e}^{4} {\mathrm e}^{\frac {\left (\left (2 x^{2}-10 x \right ) {\mathrm e}^{8}-x \right ) {\mathrm e}^{-8}}{x -5}}\right ) {\mathrm e}^{-4}}{x \left (x -5\right )}\) | \(92\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.61, size = 76, normalized size = 3.04 \begin {gather*} {\left ({\left (x - \frac {25}{x - 5} + 10 \, \log \left (x - 5\right )\right )} e^{8} + 10 \, {\left (\frac {5}{x - 5} - \log \left (x - 5\right )\right )} e^{8} - \frac {25 \, e^{8}}{x - 5} + \frac {e^{\left (2 \, x - \frac {5}{x e^{8} - 5 \, e^{8}} - e^{\left (-8\right )} + 8\right )}}{x}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.39, size = 37, normalized size = 1.48 \begin {gather*} x+\frac {{\mathrm {e}}^{-\frac {10\,x}{x-5}}\,{\mathrm {e}}^{\frac {2\,x^2}{x-5}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{-8}}{x-5}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.23, size = 24, normalized size = 0.96 \begin {gather*} x + \frac {e^{\frac {- x + \left (2 x^{2} - 10 x\right ) e^{8}}{\left (x - 5\right ) e^{8}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________