Optimal. Leaf size=35 \[ -x+\frac {\frac {e^x}{-5 e^x+\frac {x^2}{3}}+3 (1+x+\log (2))}{x} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.59, 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 {-3 x^4-x^6+e^{2 x} \left (-630-225 x^2-675 \log (2)\right )-3 x^4 \log (2)+e^x \left (81 x^2+3 x^3+30 x^4+90 x^2 \log (2)\right )}{225 e^{2 x} x^2-30 e^x x^4+x^6} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x^6+e^{2 x} \left (-630-225 x^2-675 \log (2)\right )+x^4 (-3-3 \log (2))+e^x \left (81 x^2+3 x^3+30 x^4+90 x^2 \log (2)\right )}{225 e^{2 x} x^2-30 e^x x^4+x^6} \, dx\\ &=\int \frac {-x^6+e^{2 x} \left (-630-225 x^2-675 \log (2)\right )+x^4 (-3-3 \log (2))+e^x \left (81 x^2+3 x^3+30 x^4+90 x^2 \log (2)\right )}{x^2 \left (15 e^x-x^2\right )^2} \, dx\\ &=\int \left (\frac {(-2+x) x^2}{5 \left (-15 e^x+x^2\right )^2}-\frac {-1+x}{5 \left (-15 e^x+x^2\right )}+\frac {-14-5 x^2-15 \log (2)}{5 x^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {(-2+x) x^2}{\left (-15 e^x+x^2\right )^2} \, dx-\frac {1}{5} \int \frac {-1+x}{-15 e^x+x^2} \, dx+\frac {1}{5} \int \frac {-14-5 x^2-15 \log (2)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-\frac {2 x^2}{\left (-15 e^x+x^2\right )^2}+\frac {x^3}{\left (-15 e^x+x^2\right )^2}\right ) \, dx-\frac {1}{5} \int \left (\frac {1}{15 e^x-x^2}+\frac {x}{-15 e^x+x^2}\right ) \, dx+\frac {1}{5} \int \left (-5+\frac {-14-15 \log (2)}{x^2}\right ) \, dx\\ &=-x+\frac {14+15 \log (2)}{5 x}-\frac {1}{5} \int \frac {1}{15 e^x-x^2} \, dx+\frac {1}{5} \int \frac {x^3}{\left (-15 e^x+x^2\right )^2} \, dx-\frac {1}{5} \int \frac {x}{-15 e^x+x^2} \, dx-\frac {2}{5} \int \frac {x^2}{\left (-15 e^x+x^2\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.18, size = 43, normalized size = 1.23 \begin {gather*} \frac {3 e^x \left (-14+5 x^2-15 \log (2)\right )+x^2 \left (3-x^2+\log (8)\right )}{-15 e^x x+x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.30, size = 30, normalized size = 0.86
method | result | size |
risch | \(-x +\frac {3 \ln \left (2\right )}{x}+\frac {14}{5 x}+\frac {x}{5 x^{2}-75 \,{\mathrm e}^{x}}\) | \(30\) |
norman | \(\frac {\left (-45 \ln \left (2\right )-42\right ) {\mathrm e}^{x}+\left (3 \ln \left (2\right )+3\right ) x^{2}-x^{4}+15 \,{\mathrm e}^{x} x^{2}}{x \left (x^{2}-15 \,{\mathrm e}^{x}\right )}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.52, size = 41, normalized size = 1.17 \begin {gather*} -\frac {x^{4} - 3 \, x^{2} {\left (\log \left (2\right ) + 1\right )} - 3 \, {\left (5 \, x^{2} - 15 \, \log \left (2\right ) - 14\right )} e^{x}}{x^{3} - 15 \, x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.41, size = 44, normalized size = 1.26 \begin {gather*} -\frac {x^{4} - 3 \, x^{2} \log \left (2\right ) - 3 \, x^{2} - 3 \, {\left (5 \, x^{2} - 15 \, \log \left (2\right ) - 14\right )} e^{x}}{x^{3} - 15 \, x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 26, normalized size = 0.74 \begin {gather*} - x - \frac {x}{- 5 x^{2} + 75 e^{x}} - \frac {-14 - 15 \log {\left (2 \right )}}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 46, normalized size = 1.31 \begin {gather*} -\frac {x^{4} - 15 \, x^{2} e^{x} - 3 \, x^{2} \log \left (2\right ) - 3 \, x^{2} + 45 \, e^{x} \log \left (2\right ) + 42 \, e^{x}}{x^{3} - 15 \, x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.59, size = 38, normalized size = 1.09 \begin {gather*} -x-\frac {x^2\,\left (\ln \left (8\right )+3\right )-{\mathrm {e}}^x\,\left (45\,\ln \left (2\right )+42\right )}{15\,x\,{\mathrm {e}}^x-x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________