Optimal. Leaf size=24 \[ \frac {1}{x \left (-25+e^2+e^{e^5}+x\right ) \left (x+x^2\right )} \]
________________________________________________________________________________________
Rubi [B] time = 0.31, antiderivative size = 132, normalized size of antiderivative = 5.50, number of steps used = 4, number of rules used = 2, integrand size = 165, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6, 2074} \begin {gather*} -\frac {1}{\left (25-e^2-e^{e^5}\right ) x^2}+\frac {24-e^2-e^{e^5}}{\left (25-e^2-e^{e^5}\right )^2 x}-\frac {1}{\left (26-e^2-e^{e^5}\right ) (x+1)}-\frac {1}{\left (25-e^2-e^{e^5}\right )^2 \left (26-e^2-e^{e^5}\right ) \left (-x-e^{e^5}-e^2+25\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {50+\left (e^2+e^{e^5}\right ) (-2-3 x)+72 x-4 x^2}{625 x^3+1200 x^4+526 x^5-48 x^6+x^7+e^4 \left (x^3+2 x^4+x^5\right )+e^{2 e^5} \left (x^3+2 x^4+x^5\right )+e^2 \left (-50 x^3-98 x^4-46 x^5+2 x^6\right )+e^{e^5} \left (-50 x^3-98 x^4-46 x^5+2 x^6+e^2 \left (2 x^3+4 x^4+2 x^5\right )\right )} \, dx\\ &=\int \frac {50+\left (e^2+e^{e^5}\right ) (-2-3 x)+72 x-4 x^2}{625 x^3+1200 x^4+526 x^5-48 x^6+x^7+\left (e^4+e^{2 e^5}\right ) \left (x^3+2 x^4+x^5\right )+e^2 \left (-50 x^3-98 x^4-46 x^5+2 x^6\right )+e^{e^5} \left (-50 x^3-98 x^4-46 x^5+2 x^6+e^2 \left (2 x^3+4 x^4+2 x^5\right )\right )} \, dx\\ &=\int \left (-\frac {2}{\left (-25+e^2+e^{e^5}\right ) x^3}+\frac {-24+e^2+e^{e^5}}{\left (-25+e^2+e^{e^5}\right )^2 x^2}-\frac {1}{\left (-26+e^2+e^{e^5}\right ) (1+x)^2}+\frac {1}{\left (-26+e^2+e^{e^5}\right ) \left (-25+e^2+e^{e^5}\right )^2 \left (-25+e^2+e^{e^5}+x\right )^2}\right ) \, dx\\ &=-\frac {1}{\left (25-e^2-e^{e^5}\right )^2 \left (26-e^2-e^{e^5}\right ) \left (25-e^2-e^{e^5}-x\right )}-\frac {1}{\left (25-e^2-e^{e^5}\right ) x^2}+\frac {24-e^2-e^{e^5}}{\left (25-e^2-e^{e^5}\right )^2 x}-\frac {1}{\left (26-e^2-e^{e^5}\right ) (1+x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.16, size = 22, normalized size = 0.92 \begin {gather*} \frac {1}{x^2 (1+x) \left (-25+e^2+e^{e^5}+x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 37, normalized size = 1.54 \begin {gather*} \frac {1}{x^{4} - 24 \, x^{3} - 25 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (e^{5}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 2.28, size = 20, normalized size = 0.83
method | result | size |
norman | \(\frac {1}{x^{2} \left (x +1\right ) \left ({\mathrm e}^{2}+{\mathrm e}^{{\mathrm e}^{5}}+x -25\right )}\) | \(20\) |
gosper | \(\frac {1}{x^{2} \left ({\mathrm e}^{2} x +x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}+{\mathrm e}^{2}+{\mathrm e}^{{\mathrm e}^{5}}-24 x -25\right )}\) | \(29\) |
risch | \(\frac {1}{x^{2} \left ({\mathrm e}^{2} x +x \,{\mathrm e}^{{\mathrm e}^{5}}+x^{2}+{\mathrm e}^{2}+{\mathrm e}^{{\mathrm e}^{5}}-24 x -25\right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 28, normalized size = 1.17 \begin {gather*} \frac {1}{x^{4} + x^{3} {\left (e^{2} + e^{\left (e^{5}\right )} - 24\right )} + x^{2} {\left (e^{2} + e^{\left (e^{5}\right )} - 25\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 5.69, size = 31, normalized size = 1.29 \begin {gather*} \frac {1}{x^{4} + x^{3} \left (-24 + e^{2} + e^{e^{5}}\right ) + x^{2} \left (-25 + e^{2} + e^{e^{5}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________