Optimal. Leaf size=25 \[ \frac {1}{\left (x+\frac {225 \left (2+e^x\right ) \left (-x+4 x^2\right )^2}{x^2}\right )^2} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.79, 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 {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {7198-28800 x-450 e^x \left (-7+24 x+16 x^2\right )}{\left (450+225 e^x (1-4 x)^2-3599 x+7200 x^2\right )^3} \, dx\\ &=\int \left (-\frac {2 (7+4 x)}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2}+\frac {2 \left (-449+5403 x-21596 x^2+28800 x^3\right )}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3}\right ) \, dx\\ &=-\left (2 \int \frac {7+4 x}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2} \, dx\right )+2 \int \frac {-449+5403 x-21596 x^2+28800 x^3}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3} \, dx\\ &=2 \int \left (\frac {451}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3}-\frac {3599 x}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3}+\frac {7200 x^2}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3}+\frac {2}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3}\right ) \, dx-2 \int \left (\frac {1}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2}+\frac {8}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {1}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2} \, dx\right )+4 \int \frac {1}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3} \, dx-16 \int \frac {1}{(-1+4 x) \left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^2} \, dx+902 \int \frac {1}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3} \, dx-7198 \int \frac {x}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3} \, dx+14400 \int \frac {x^2}{\left (450+225 e^x-3599 x-1800 e^x x+7200 x^2+3600 e^x x^2\right )^3} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.15, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{\left (450+225 e^x (1-4 x)^2-3599 x+7200 x^2\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.46, size = 29, normalized size = 1.16
method | result | size |
norman | \(\frac {1}{\left (3600 \,{\mathrm e}^{x} x^{2}-1800 \,{\mathrm e}^{x} x +7200 x^{2}+225 \,{\mathrm e}^{x}-3599 x +450\right )^{2}}\) | \(29\) |
risch | \(\frac {1}{\left (3600 \,{\mathrm e}^{x} x^{2}-1800 \,{\mathrm e}^{x} x +7200 x^{2}+225 \,{\mathrm e}^{x}-3599 x +450\right )^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (24) = 48\).
time = 0.43, size = 72, normalized size = 2.88 \begin {gather*} \frac {1}{51840000 \, x^{4} - 51825600 \, x^{3} + 19432801 \, x^{2} + 50625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} e^{\left (2 \, x\right )} + 450 \, {\left (115200 \, x^{4} - 115184 \, x^{3} + 43192 \, x^{2} - 7199 \, x + 450\right )} e^{x} - 3239100 \, x + 202500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (24) = 48\).
time = 0.38, size = 72, normalized size = 2.88 \begin {gather*} \frac {1}{51840000 \, x^{4} - 51825600 \, x^{3} + 19432801 \, x^{2} + 50625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} e^{\left (2 \, x\right )} + 450 \, {\left (115200 \, x^{4} - 115184 \, x^{3} + 43192 \, x^{2} - 7199 \, x + 450\right )} e^{x} - 3239100 \, x + 202500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 70 vs.
\(2 (22) = 44\).
time = 0.34, size = 70, normalized size = 2.80 \begin {gather*} \frac {1}{51840000 x^{4} - 51825600 x^{3} + 19432801 x^{2} - 3239100 x + \left (12960000 x^{4} - 12960000 x^{3} + 4860000 x^{2} - 810000 x + 50625\right ) e^{2 x} + \left (51840000 x^{4} - 51832800 x^{3} + 19436400 x^{2} - 3239550 x + 202500\right ) e^{x} + 202500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 92 vs.
\(2 (24) = 48\).
time = 0.43, size = 92, normalized size = 3.68 \begin {gather*} \frac {1}{12960000 \, x^{4} e^{\left (2 \, x\right )} + 51840000 \, x^{4} e^{x} + 51840000 \, x^{4} - 12960000 \, x^{3} e^{\left (2 \, x\right )} - 51832800 \, x^{3} e^{x} - 51825600 \, x^{3} + 4860000 \, x^{2} e^{\left (2 \, x\right )} + 19436400 \, x^{2} e^{x} + 19432801 \, x^{2} - 810000 \, x e^{\left (2 \, x\right )} - 3239550 \, x e^{x} - 3239100 \, x + 50625 \, e^{\left (2 \, x\right )} + 202500 \, e^{x} + 202500} \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 {28800\,x+{\mathrm {e}}^x\,\left (7200\,x^2+10800\,x-3150\right )-7198}{{\mathrm {e}}^{3\,x}\,\left (46656000000\,x^6-69984000000\,x^5+43740000000\,x^4-14580000000\,x^3+2733750000\,x^2-273375000\,x+11390625\right )-2186392500\,x+{\mathrm {e}}^{2\,x}\,\left (279936000000\,x^6-419865120000\,x^5+262401120000\,x^4-87465420000\,x^3+16400070000\,x^2-1640098125\,x+68343750\right )+{\mathrm {e}}^x\,\left (559872000000\,x^6-839652480000\,x^5+524724490800\,x^4-174901685400\,x^3+32795280675\,x^2-3279892500\,x+136687500\right )+21860281350\,x^2-116581690799\,x^3+349764501600\,x^4-559716480000\,x^5+373248000000\,x^6+91125000} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________