Optimal. Leaf size=28 \[ \frac {x (5+x)}{5-e^x-\frac {3}{3-x}+\frac {x}{2}} \]
________________________________________________________________________________________
Rubi [F] time = 1.39, 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 {720-192 x-86 x^2+28 x^3+2 x^4+e^x \left (-180+228 x-56 x^2-12 x^3+4 x^4\right )}{576-336 x+x^2+14 x^3+x^4+e^{2 x} \left (36-24 x+4 x^2\right )+e^x \left (-288+180 x-16 x^2-4 x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (360-96 x-43 x^2+14 x^3+x^4+2 e^x (-3+x)^2 \left (-5+3 x+x^2\right )\right )}{\left (24+2 e^x (-3+x)-7 x-x^2\right )^2} \, dx\\ &=2 \int \frac {360-96 x-43 x^2+14 x^3+x^4+2 e^x (-3+x)^2 \left (-5+3 x+x^2\right )}{\left (24+2 e^x (-3+x)-7 x-x^2\right )^2} \, dx\\ &=2 \int \left (\frac {15-14 x+x^3}{24-6 e^x-7 x+2 e^x x-x^2}+\frac {x \left (345-126 x-24 x^2+8 x^3+x^4\right )}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}\right ) \, dx\\ &=2 \int \frac {15-14 x+x^3}{24-6 e^x-7 x+2 e^x x-x^2} \, dx+2 \int \frac {x \left (345-126 x-24 x^2+8 x^3+x^4\right )}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx\\ &=2 \int \left (\frac {345 x}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}-\frac {126 x^2}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}-\frac {24 x^3}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}+\frac {8 x^4}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}+\frac {x^5}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2}\right ) \, dx+2 \int \left (\frac {15}{24-6 e^x-7 x+2 e^x x-x^2}+\frac {14 x}{-24+6 e^x+7 x-2 e^x x+x^2}-\frac {x^3}{-24+6 e^x+7 x-2 e^x x+x^2}\right ) \, dx\\ &=2 \int \frac {x^5}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx-2 \int \frac {x^3}{-24+6 e^x+7 x-2 e^x x+x^2} \, dx+16 \int \frac {x^4}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx+28 \int \frac {x}{-24+6 e^x+7 x-2 e^x x+x^2} \, dx+30 \int \frac {1}{24-6 e^x-7 x+2 e^x x-x^2} \, dx-48 \int \frac {x^3}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx-252 \int \frac {x^2}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx+690 \int \frac {x}{\left (-24+6 e^x+7 x-2 e^x x+x^2\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.43, size = 27, normalized size = 0.96 \begin {gather*} \frac {2 (-3+x) x (5+x)}{-24-2 e^x (-3+x)+7 x+x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 31, normalized size = 1.11 \begin {gather*} \frac {2 \, {\left (x^{3} + 2 \, x^{2} - 15 \, x\right )}}{x^{2} - 2 \, {\left (x - 3\right )} e^{x} + 7 \, x - 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 33, normalized size = 1.18 \begin {gather*} \frac {2 \, {\left (x^{3} + 2 \, x^{2} - 15 \, x\right )}}{x^{2} - 2 \, x e^{x} + 7 \, x + 6 \, e^{x} - 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 29, normalized size = 1.04
method | result | size |
risch | \(\frac {2 \left (x -3\right ) \left (5+x \right ) x}{x^{2}-2 \,{\mathrm e}^{x} x +7 x +6 \,{\mathrm e}^{x}-24}\) | \(29\) |
norman | \(\frac {2 x^{3}+4 x^{2}-30 x}{x^{2}-2 \,{\mathrm e}^{x} x +7 x +6 \,{\mathrm e}^{x}-24}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 31, normalized size = 1.11 \begin {gather*} \frac {2 \, {\left (x^{3} + 2 \, x^{2} - 15 \, x\right )}}{x^{2} - 2 \, {\left (x - 3\right )} e^{x} + 7 \, x - 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {192\,x+{\mathrm {e}}^x\,\left (-4\,x^4+12\,x^3+56\,x^2-228\,x+180\right )+86\,x^2-28\,x^3-2\,x^4-720}{{\mathrm {e}}^{2\,x}\,\left (4\,x^2-24\,x+36\right )-336\,x+x^2+14\,x^3+x^4-{\mathrm {e}}^x\,\left (4\,x^3+16\,x^2-180\,x+288\right )+576} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 29, normalized size = 1.04 \begin {gather*} \frac {- 2 x^{3} - 4 x^{2} + 30 x}{- x^{2} - 7 x + \left (2 x - 6\right ) e^{x} + 24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________