Optimal. Leaf size=30 \[ (-2+\log (x)) \log \left (x \left (e^x+(x-4 x (2-i \pi -\log (3)))^2\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 3.86, 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^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+16 x^3 (i \pi +\log (3))^2+x^3 (49-56 (i \pi +\log (3)))} \, dx\\ &=\int \frac {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {e^x (-2-2 x)-96 x^2 (i \pi +\log (3))^2+x^2 (-294+336 (i \pi +\log (3)))+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {e^x (-2-2 x)+x^2 \left (-294+336 (i \pi +\log (3))-96 (i \pi +\log (3))^2\right )+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {-2 e^x (1+x)+6 x^2 (7 i+4 \pi -4 i \log (3))^2+\left (e^x (1+x)-3 x^2 (7 i+4 \pi -4 i \log (3))^2\right ) \log (x)+\left (e^x-x^2 (7 i+4 \pi -4 i \log (3))^2\right ) \log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2} \, dx\\ &=\int \left (\frac {(2-x) x (7 i+4 \pi -4 i \log (3))^2 (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {-2-2 x+\log (x)+x \log (x)+\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x}\right ) \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \frac {(2-x) x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {-2-2 x+\log (x)+x \log (x)+\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \left (\frac {2 x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x^2 (-2+\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\int \left (\frac {(1+x) (-2+\log (x))}{x}+\frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x}\right ) \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \frac {x^2 (-2+\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {(1+x) (-2+\log (x))}{x} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \left (\frac {2 x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x^2 \log (x)}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \left (\frac {2 x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x \log (x)}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\int (-2+\log (x)) \, dx+\int \frac {-2+\log (x)}{x} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-2 x+\frac {1}{2} (2-\log (x))^2+(7 i+4 \pi -4 i \log (3))^2 \int \frac {x^2 \log (x)}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x \log (x)}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \log (x) \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-3 x+\frac {1}{2} (2-\log (x))^2+x \log (x)-(7 i+4 \pi -4 i \log (3))^2 \int \frac {\int \frac {x^2}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx-\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {\int -\frac {x}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left ((7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x^2}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-3 x+\frac {1}{2} (2-\log (x))^2+x \log (x)-(7 i+4 \pi -4 i \log (3))^2 \int \frac {\int \frac {x^2}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {\int \frac {x}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left ((7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x^2}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.21, size = 216, normalized size = 7.20 \begin {gather*} 2 i \tan ^{-1}\left (\frac {8 \pi x^2 (-7+4 \log (3))}{-e^x-49 x^2+16 \pi ^2 x^2+56 x^2 \log (3)-16 x^2 \log ^2(3)}\right )-2 \log (x)+\log (x) \log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )-\log \left (e^{2 x}+98 e^x x^2-32 e^x \pi ^2 x^2+2401 x^4+1568 \pi ^2 x^4+256 \pi ^4 x^4-112 e^x x^2 \log (3)-5488 x^4 \log (3)-1792 \pi ^2 x^4 \log (3)+32 e^x x^2 \log ^2(3)+4704 x^4 \log ^2(3)+512 \pi ^2 x^4 \log ^2(3)-1792 x^4 \log ^3(3)+256 x^4 \log ^4(3)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.75, size = 46, normalized size = 1.53 \begin {gather*} {\left (\log \relax (x) - 2\right )} \log \left (-8 \, {\left (-4 i \, \pi + 7\right )} x^{3} \log \relax (3) + 16 \, x^{3} \log \relax (3)^{2} + {\left (-56 i \, \pi - 16 \, \pi ^{2} + 49\right )} x^{3} + x e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.46, size = 108, normalized size = 3.60 \begin {gather*} \log \left (-16 \, \pi ^{2} x^{2} + 32 i \, \pi x^{2} \log \relax (3) + 16 \, x^{2} \log \relax (3)^{2} - 56 i \, \pi x^{2} - 56 \, x^{2} \log \relax (3) + 49 \, x^{2} + e^{x}\right ) \log \relax (x) + \log \relax (x)^{2} - 2 \, \log \left (-16 \, \pi ^{2} x^{2} + 32 i \, \pi x^{2} \log \relax (3) + 16 \, x^{2} \log \relax (3)^{2} - 56 i \, \pi x^{2} - 56 \, x^{2} \log \relax (3) + 49 \, x^{2} + e^{x}\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.77, size = 483, normalized size = 16.10
method | result | size |
risch | \(\ln \relax (x ) \ln \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )+\ln \relax (x )^{2}-\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )}{2}+\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{2}}{2}+\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{2}}{2}-\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{3}}{2}-2 \ln \relax (x )-2 \ln \left (-16 \pi ^{2} x^{2}+32 i \pi \ln \relax (3) x^{2}-56 i \pi \,x^{2}+16 x^{2} \ln \relax (3)^{2}-56 x^{2} \ln \relax (3)+49 x^{2}+{\mathrm e}^{x}\right )\) | \(483\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 47, normalized size = 1.57 \begin {gather*} {\left (\log \relax (x) - 2\right )} \log \left ({\left (-56 i \, \pi - 16 \, \pi ^{2} - 8 \, {\left (-4 i \, \pi + 7\right )} \log \relax (3) + 16 \, \log \relax (3)^{2} + 49\right )} x^{2} + e^{x}\right ) + \log \relax (x)^{2} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {96\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-\ln \left (16\,x^3\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^3\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+x\,{\mathrm {e}}^x+49\,x^3\right )\,\left ({\mathrm {e}}^x+16\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+49\,x^2\right )+{\mathrm {e}}^x\,\left (2\,x+2\right )-336\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )-\ln \relax (x)\,\left (48\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2+{\mathrm {e}}^x\,\left (x+1\right )-168\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+147\,x^2\right )+294\,x^2}{16\,x^3\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^3\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+x\,{\mathrm {e}}^x+49\,x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________