3.89.36 \(\int \frac {-800 x+80 e^{2 x} x-2 e^{4 x} x+(-800+80 e^{2 x}-800 x^2+e^{4 x} (-2+2 x^2)) \log (x)+(800+1600 x+2400 x^2+e^{2 x} (-80-320 x-400 x^2-160 x^3)+e^{4 x} (2+12 x+14 x^2+8 x^3)) \log ^2(x)+(675+2400 x+2400 x^2+1600 x^3+e^{2 x} (-160-400 x-480 x^2-320 x^3-80 x^4)+e^{4 x} (6+14 x+18 x^2+12 x^3+4 x^4)) \log ^3(x)}{25 \log ^3(x)} \, dx\)

Optimal. Leaf size=32 \[ -5 x+\left (-4+\frac {e^{2 x}}{5}\right )^2 \left (1+x+x^2+\frac {x}{\log (x)}\right )^2 \]

________________________________________________________________________________________

Rubi [F]  time = 18.71, 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 {-800 x+80 e^{2 x} x-2 e^{4 x} x+\left (-800+80 e^{2 x}-800 x^2+e^{4 x} \left (-2+2 x^2\right )\right ) \log (x)+\left (800+1600 x+2400 x^2+e^{2 x} \left (-80-320 x-400 x^2-160 x^3\right )+e^{4 x} \left (2+12 x+14 x^2+8 x^3\right )\right ) \log ^2(x)+\left (675+2400 x+2400 x^2+1600 x^3+e^{2 x} \left (-160-400 x-480 x^2-320 x^3-80 x^4\right )+e^{4 x} \left (6+14 x+18 x^2+12 x^3+4 x^4\right )\right ) \log ^3(x)}{25 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-800*x + 80*E^(2*x)*x - 2*E^(4*x)*x + (-800 + 80*E^(2*x) - 800*x^2 + E^(4*x)*(-2 + 2*x^2))*Log[x] + (800
+ 1600*x + 2400*x^2 + E^(2*x)*(-80 - 320*x - 400*x^2 - 160*x^3) + E^(4*x)*(2 + 12*x + 14*x^2 + 8*x^3))*Log[x]^
2 + (675 + 2400*x + 2400*x^2 + 1600*x^3 + E^(2*x)*(-160 - 400*x - 480*x^2 - 320*x^3 - 80*x^4) + E^(4*x)*(6 + 1
4*x + 18*x^2 + 12*x^3 + 4*x^4))*Log[x]^3)/(25*Log[x]^3),x]

[Out]

(-8*E^(2*x))/5 + E^(4*x)/25 + 27*x - (16*E^(2*x)*x)/5 + (2*E^(4*x)*x)/25 + 48*x^2 - (24*E^(2*x)*x^2)/5 + (3*E^
(4*x)*x^2)/25 + 32*x^3 - (16*E^(2*x)*x^3)/5 + (2*E^(4*x)*x^3)/25 + 16*x^4 - (8*E^(2*x)*x^4)/5 + (E^(4*x)*x^4)/
25 + (16*x^2)/Log[x]^2 + (32*x)/Log[x] + (32*x^2)/Log[x] + (32*x^3)/Log[x] + (16*Defer[Int][(E^(2*x)*x)/Log[x]
^3, x])/5 - (2*Defer[Int][(E^(4*x)*x)/Log[x]^3, x])/25 + (16*Defer[Int][E^(2*x)/Log[x]^2, x])/5 - (2*Defer[Int
][E^(4*x)/Log[x]^2, x])/25 + (2*Defer[Int][(E^(4*x)*x^2)/Log[x]^2, x])/25 - (16*Defer[Int][E^(2*x)/Log[x], x])
/5 + (2*Defer[Int][E^(4*x)/Log[x], x])/25 - (64*Defer[Int][(E^(2*x)*x)/Log[x], x])/5 + (12*Defer[Int][(E^(4*x)
*x)/Log[x], x])/25 - 16*Defer[Int][(E^(2*x)*x^2)/Log[x], x] + (14*Defer[Int][(E^(4*x)*x^2)/Log[x], x])/25 - (3
2*Defer[Int][(E^(2*x)*x^3)/Log[x], x])/5 + (8*Defer[Int][(E^(4*x)*x^3)/Log[x], x])/25

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {-800 x+80 e^{2 x} x-2 e^{4 x} x+\left (-800+80 e^{2 x}-800 x^2+e^{4 x} \left (-2+2 x^2\right )\right ) \log (x)+\left (800+1600 x+2400 x^2+e^{2 x} \left (-80-320 x-400 x^2-160 x^3\right )+e^{4 x} \left (2+12 x+14 x^2+8 x^3\right )\right ) \log ^2(x)+\left (675+2400 x+2400 x^2+1600 x^3+e^{2 x} \left (-160-400 x-480 x^2-320 x^3-80 x^4\right )+e^{4 x} \left (6+14 x+18 x^2+12 x^3+4 x^4\right )\right ) \log ^3(x)}{\log ^3(x)} \, dx\\ &=\frac {1}{25} \int \left (\frac {25 \left (-32 x-32 \log (x)-32 x^2 \log (x)+32 \log ^2(x)+64 x \log ^2(x)+96 x^2 \log ^2(x)+27 \log ^3(x)+96 x \log ^3(x)+96 x^2 \log ^3(x)+64 x^3 \log ^3(x)\right )}{\log ^3(x)}-\frac {80 e^{2 x} \left (-x-\log (x)+\log ^2(x)+4 x \log ^2(x)+5 x^2 \log ^2(x)+2 x^3 \log ^2(x)+2 \log ^3(x)+5 x \log ^3(x)+6 x^2 \log ^3(x)+4 x^3 \log ^3(x)+x^4 \log ^3(x)\right )}{\log ^3(x)}+\frac {2 e^{4 x} \left (-x-\log (x)+x^2 \log (x)+\log ^2(x)+6 x \log ^2(x)+7 x^2 \log ^2(x)+4 x^3 \log ^2(x)+3 \log ^3(x)+7 x \log ^3(x)+9 x^2 \log ^3(x)+6 x^3 \log ^3(x)+2 x^4 \log ^3(x)\right )}{\log ^3(x)}\right ) \, dx\\ &=\frac {2}{25} \int \frac {e^{4 x} \left (-x-\log (x)+x^2 \log (x)+\log ^2(x)+6 x \log ^2(x)+7 x^2 \log ^2(x)+4 x^3 \log ^2(x)+3 \log ^3(x)+7 x \log ^3(x)+9 x^2 \log ^3(x)+6 x^3 \log ^3(x)+2 x^4 \log ^3(x)\right )}{\log ^3(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} \left (-x-\log (x)+\log ^2(x)+4 x \log ^2(x)+5 x^2 \log ^2(x)+2 x^3 \log ^2(x)+2 \log ^3(x)+5 x \log ^3(x)+6 x^2 \log ^3(x)+4 x^3 \log ^3(x)+x^4 \log ^3(x)\right )}{\log ^3(x)} \, dx+\int \frac {-32 x-32 \log (x)-32 x^2 \log (x)+32 \log ^2(x)+64 x \log ^2(x)+96 x^2 \log ^2(x)+27 \log ^3(x)+96 x \log ^3(x)+96 x^2 \log ^3(x)+64 x^3 \log ^3(x)}{\log ^3(x)} \, dx\\ &=\frac {2}{25} \int \frac {e^{4 x} \left (-x+\left (-1+x^2\right ) \log (x)+\left (1+6 x+7 x^2+4 x^3\right ) \log ^2(x)+\left (3+7 x+9 x^2+6 x^3+2 x^4\right ) \log ^3(x)\right )}{\log ^3(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} \left (-x-\log (x)+(1+x)^2 (1+2 x) \log ^2(x)+\left (2+5 x+6 x^2+4 x^3+x^4\right ) \log ^3(x)\right )}{\log ^3(x)} \, dx+\int \left (27+96 x+96 x^2+64 x^3-\frac {32 x}{\log ^3(x)}-\frac {32 \left (1+x^2\right )}{\log ^2(x)}+\frac {32 \left (1+2 x+3 x^2\right )}{\log (x)}\right ) \, dx\\ &=27 x+48 x^2+32 x^3+16 x^4+\frac {2}{25} \int \left (3 e^{4 x}+7 e^{4 x} x+9 e^{4 x} x^2+6 e^{4 x} x^3+2 e^{4 x} x^4-\frac {e^{4 x} x}{\log ^3(x)}+\frac {e^{4 x} \left (-1+x^2\right )}{\log ^2(x)}+\frac {e^{4 x} \left (1+6 x+7 x^2+4 x^3\right )}{\log (x)}\right ) \, dx-\frac {16}{5} \int \left (2 e^{2 x}+5 e^{2 x} x+6 e^{2 x} x^2+4 e^{2 x} x^3+e^{2 x} x^4-\frac {e^{2 x} x}{\log ^3(x)}-\frac {e^{2 x}}{\log ^2(x)}+\frac {e^{2 x} (1+x)^2 (1+2 x)}{\log (x)}\right ) \, dx-32 \int \frac {x}{\log ^3(x)} \, dx-32 \int \frac {1+x^2}{\log ^2(x)} \, dx+32 \int \frac {1+2 x+3 x^2}{\log (x)} \, dx\\ &=27 x+48 x^2+32 x^3+16 x^4+\frac {16 x^2}{\log ^2(x)}-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} \left (-1+x^2\right )}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} \left (1+6 x+7 x^2+4 x^3\right )}{\log (x)} \, dx+\frac {4}{25} \int e^{4 x} x^4 \, dx+\frac {6}{25} \int e^{4 x} \, dx+\frac {12}{25} \int e^{4 x} x^3 \, dx+\frac {14}{25} \int e^{4 x} x \, dx+\frac {18}{25} \int e^{4 x} x^2 \, dx-\frac {16}{5} \int e^{2 x} x^4 \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x} (1+x)^2 (1+2 x)}{\log (x)} \, dx-\frac {32}{5} \int e^{2 x} \, dx-\frac {64}{5} \int e^{2 x} x^3 \, dx-16 \int e^{2 x} x \, dx-\frac {96}{5} \int e^{2 x} x^2 \, dx-32 \int \left (\frac {1}{\log ^2(x)}+\frac {x^2}{\log ^2(x)}\right ) \, dx+32 \int \left (\frac {1}{\log (x)}+\frac {2 x}{\log (x)}+\frac {3 x^2}{\log (x)}\right ) \, dx-32 \int \frac {x}{\log ^2(x)} \, dx\\ &=-\frac {16 e^{2 x}}{5}+\frac {3 e^{4 x}}{50}+27 x-8 e^{2 x} x+\frac {7}{50} e^{4 x} x+48 x^2-\frac {48}{5} e^{2 x} x^2+\frac {9}{50} e^{4 x} x^2+32 x^3-\frac {32}{5} e^{2 x} x^3+\frac {3}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x^2}{\log (x)}+\frac {2}{25} \int \left (-\frac {e^{4 x}}{\log ^2(x)}+\frac {e^{4 x} x^2}{\log ^2(x)}\right ) \, dx+\frac {2}{25} \int \left (\frac {e^{4 x}}{\log (x)}+\frac {6 e^{4 x} x}{\log (x)}+\frac {7 e^{4 x} x^2}{\log (x)}+\frac {4 e^{4 x} x^3}{\log (x)}\right ) \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {7}{50} \int e^{4 x} \, dx-\frac {4}{25} \int e^{4 x} x^3 \, dx-\frac {9}{25} \int e^{4 x} x \, dx-\frac {9}{25} \int e^{4 x} x^2 \, dx-\frac {16}{5} \int \left (\frac {e^{2 x}}{\log (x)}+\frac {4 e^{2 x} x}{\log (x)}+\frac {5 e^{2 x} x^2}{\log (x)}+\frac {2 e^{2 x} x^3}{\log (x)}\right ) \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx+\frac {32}{5} \int e^{2 x} x^3 \, dx+8 \int e^{2 x} \, dx+\frac {96}{5} \int e^{2 x} x \, dx+\frac {96}{5} \int e^{2 x} x^2 \, dx-32 \int \frac {1}{\log ^2(x)} \, dx-32 \int \frac {x^2}{\log ^2(x)} \, dx+32 \int \frac {1}{\log (x)} \, dx+96 \int \frac {x^2}{\log (x)} \, dx\\ &=\frac {4 e^{2 x}}{5}+\frac {e^{4 x}}{40}+27 x+\frac {8}{5} e^{2 x} x+\frac {1}{20} e^{4 x} x+48 x^2+\frac {9}{100} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}+32 \text {li}(x)-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {9}{100} \int e^{4 x} \, dx+\frac {3}{25} \int e^{4 x} x^2 \, dx+\frac {9}{50} \int e^{4 x} x \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {48}{5} \int e^{2 x} \, dx-\frac {48}{5} \int e^{2 x} x^2 \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx-\frac {96}{5} \int e^{2 x} x \, dx-32 \int \frac {1}{\log (x)} \, dx-96 \int \frac {x^2}{\log (x)} \, dx+96 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )\\ &=-4 e^{2 x}+\frac {19 e^{4 x}}{400}+27 x-8 e^{2 x} x+\frac {19}{200} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+96 \text {Ei}(3 \log (x))+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}-\frac {9}{200} \int e^{4 x} \, dx-\frac {3}{50} \int e^{4 x} x \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx+\frac {48}{5} \int e^{2 x} \, dx+\frac {48}{5} \int e^{2 x} x \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx-96 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {4 e^{2 x}}{5}+\frac {29 e^{4 x}}{800}+27 x-\frac {16}{5} e^{2 x} x+\frac {2}{25} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}+\frac {3}{200} \int e^{4 x} \, dx-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {24}{5} \int e^{2 x} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx\\ &=-\frac {8 e^{2 x}}{5}+\frac {e^{4 x}}{25}+27 x-\frac {16}{5} e^{2 x} x+\frac {2}{25} e^{4 x} x+48 x^2-\frac {24}{5} e^{2 x} x^2+\frac {3}{25} e^{4 x} x^2+32 x^3-\frac {16}{5} e^{2 x} x^3+\frac {2}{25} e^{4 x} x^3+16 x^4-\frac {8}{5} e^{2 x} x^4+\frac {1}{25} e^{4 x} x^4+\frac {16 x^2}{\log ^2(x)}+\frac {32 x}{\log (x)}+\frac {32 x^2}{\log (x)}+\frac {32 x^3}{\log (x)}-\frac {2}{25} \int \frac {e^{4 x} x}{\log ^3(x)} \, dx-\frac {2}{25} \int \frac {e^{4 x}}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x} x^2}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {e^{4 x}}{\log (x)} \, dx+\frac {8}{25} \int \frac {e^{4 x} x^3}{\log (x)} \, dx+\frac {12}{25} \int \frac {e^{4 x} x}{\log (x)} \, dx+\frac {14}{25} \int \frac {e^{4 x} x^2}{\log (x)} \, dx+\frac {16}{5} \int \frac {e^{2 x} x}{\log ^3(x)} \, dx+\frac {16}{5} \int \frac {e^{2 x}}{\log ^2(x)} \, dx-\frac {16}{5} \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {32}{5} \int \frac {e^{2 x} x^3}{\log (x)} \, dx-\frac {64}{5} \int \frac {e^{2 x} x}{\log (x)} \, dx-16 \int \frac {e^{2 x} x^2}{\log (x)} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.16, size = 91, normalized size = 2.84 \begin {gather*} \frac {1}{25} \left (675 x+1200 x^2+800 x^3+400 x^4-40 e^{2 x} \left (1+x+x^2\right )^2+e^{4 x} \left (1+x+x^2\right )^2+\frac {\left (-20+e^{2 x}\right )^2 x^2}{\log ^2(x)}+\frac {2 \left (-20+e^{2 x}\right )^2 x \left (1+x+x^2\right )}{\log (x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-800*x + 80*E^(2*x)*x - 2*E^(4*x)*x + (-800 + 80*E^(2*x) - 800*x^2 + E^(4*x)*(-2 + 2*x^2))*Log[x] +
(800 + 1600*x + 2400*x^2 + E^(2*x)*(-80 - 320*x - 400*x^2 - 160*x^3) + E^(4*x)*(2 + 12*x + 14*x^2 + 8*x^3))*L
og[x]^2 + (675 + 2400*x + 2400*x^2 + 1600*x^3 + E^(2*x)*(-160 - 400*x - 480*x^2 - 320*x^3 - 80*x^4) + E^(4*x)*
(6 + 14*x + 18*x^2 + 12*x^3 + 4*x^4))*Log[x]^3)/(25*Log[x]^3),x]

[Out]

(675*x + 1200*x^2 + 800*x^3 + 400*x^4 - 40*E^(2*x)*(1 + x + x^2)^2 + E^(4*x)*(1 + x + x^2)^2 + ((-20 + E^(2*x)
)^2*x^2)/Log[x]^2 + (2*(-20 + E^(2*x))^2*x*(1 + x + x^2))/Log[x])/25

________________________________________________________________________________________

fricas [B]  time = 0.52, size = 145, normalized size = 4.53 \begin {gather*} \frac {x^{2} e^{\left (4 \, x\right )} - 40 \, x^{2} e^{\left (2 \, x\right )} + {\left (400 \, x^{4} + 800 \, x^{3} + 1200 \, x^{2} + {\left (x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right )} e^{\left (2 \, x\right )} + 675 \, x\right )} \log \relax (x)^{2} + 400 \, x^{2} + 2 \, {\left (400 \, x^{3} + 400 \, x^{2} + {\left (x^{3} + x^{2} + x\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{3} + x^{2} + x\right )} e^{\left (2 \, x\right )} + 400 \, x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((4*x^4+12*x^3+18*x^2+14*x+6)*exp(x)^4+(-80*x^4-320*x^3-480*x^2-400*x-160)*exp(x)^2+1600*x^3+2
400*x^2+2400*x+675)*log(x)^3+((8*x^3+14*x^2+12*x+2)*exp(x)^4+(-160*x^3-400*x^2-320*x-80)*exp(x)^2+2400*x^2+160
0*x+800)*log(x)^2+((2*x^2-2)*exp(x)^4+80*exp(x)^2-800*x^2-800)*log(x)-2*x*exp(x)^4+80*x*exp(x)^2-800*x)/log(x)
^3,x, algorithm="fricas")

[Out]

1/25*(x^2*e^(4*x) - 40*x^2*e^(2*x) + (400*x^4 + 800*x^3 + 1200*x^2 + (x^4 + 2*x^3 + 3*x^2 + 2*x + 1)*e^(4*x) -
40*(x^4 + 2*x^3 + 3*x^2 + 2*x + 1)*e^(2*x) + 675*x)*log(x)^2 + 400*x^2 + 2*(400*x^3 + 400*x^2 + (x^3 + x^2 +
x)*e^(4*x) - 40*(x^3 + x^2 + x)*e^(2*x) + 400*x)*log(x))/log(x)^2

________________________________________________________________________________________

giac [B]  time = 0.27, size = 294, normalized size = 9.19 \begin {gather*} 16 \, x^{4} + 32 \, x^{3} + 48 \, x^{2} + \frac {1}{800} \, {\left (32 \, x^{4} - 32 \, x^{3} + 24 \, x^{2} - 12 \, x + 3\right )} e^{\left (4 \, x\right )} + \frac {3}{800} \, {\left (32 \, x^{3} - 24 \, x^{2} + 12 \, x - 3\right )} e^{\left (4 \, x\right )} + \frac {9}{400} \, {\left (8 \, x^{2} - 4 \, x + 1\right )} e^{\left (4 \, x\right )} + \frac {7}{200} \, {\left (4 \, x - 1\right )} e^{\left (4 \, x\right )} - \frac {4}{5} \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} - \frac {8}{5} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} - \frac {24}{5} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + 27 \, x + \frac {2 \, x^{3} e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x^{3} e^{\left (2 \, x\right )} \log \relax (x) + 2 \, x^{2} e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x) + x^{2} e^{\left (4 \, x\right )} - 40 \, x^{2} e^{\left (2 \, x\right )} + 2 \, x e^{\left (4 \, x\right )} \log \relax (x) - 80 \, x e^{\left (2 \, x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} + \frac {16 \, {\left (2 \, x^{3} \log \relax (x) + 2 \, x^{2} \log \relax (x) + x^{2} + 2 \, x \log \relax (x)\right )}}{\log \relax (x)^{2}} + \frac {3}{50} \, e^{\left (4 \, x\right )} - \frac {16}{5} \, e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((4*x^4+12*x^3+18*x^2+14*x+6)*exp(x)^4+(-80*x^4-320*x^3-480*x^2-400*x-160)*exp(x)^2+1600*x^3+2
400*x^2+2400*x+675)*log(x)^3+((8*x^3+14*x^2+12*x+2)*exp(x)^4+(-160*x^3-400*x^2-320*x-80)*exp(x)^2+2400*x^2+160
0*x+800)*log(x)^2+((2*x^2-2)*exp(x)^4+80*exp(x)^2-800*x^2-800)*log(x)-2*x*exp(x)^4+80*x*exp(x)^2-800*x)/log(x)
^3,x, algorithm="giac")

[Out]

16*x^4 + 32*x^3 + 48*x^2 + 1/800*(32*x^4 - 32*x^3 + 24*x^2 - 12*x + 3)*e^(4*x) + 3/800*(32*x^3 - 24*x^2 + 12*x
- 3)*e^(4*x) + 9/400*(8*x^2 - 4*x + 1)*e^(4*x) + 7/200*(4*x - 1)*e^(4*x) - 4/5*(2*x^4 - 4*x^3 + 6*x^2 - 6*x +
3)*e^(2*x) - 8/5*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x) - 24/5*(2*x^2 - 2*x + 1)*e^(2*x) - 4*(2*x - 1)*e^(2*x) + 2
7*x + 1/25*(2*x^3*e^(4*x)*log(x) - 80*x^3*e^(2*x)*log(x) + 2*x^2*e^(4*x)*log(x) - 80*x^2*e^(2*x)*log(x) + x^2*
e^(4*x) - 40*x^2*e^(2*x) + 2*x*e^(4*x)*log(x) - 80*x*e^(2*x)*log(x))/log(x)^2 + 16*(2*x^3*log(x) + 2*x^2*log(x
) + x^2 + 2*x*log(x))/log(x)^2 + 3/50*e^(4*x) - 16/5*e^(2*x)

________________________________________________________________________________________

maple [B]  time = 0.07, size = 196, normalized size = 6.12

method	result	size
risch	\(\frac {x^{4} {\mathrm e}^{4 x}}{25}+\frac {2 x^{3} {\mathrm e}^{4 x}}{25}-\frac {8 \,{\mathrm e}^{2 x} x^{4}}{5}+\frac {3 x^{2} {\mathrm e}^{4 x}}{25}-\frac {16 \,{\mathrm e}^{2 x} x^{3}}{5}+\frac {2 x \,{\mathrm e}^{4 x}}{25}+16 x^{4}-\frac {24 \,{\mathrm e}^{2 x} x^{2}}{5}+\frac {{\mathrm e}^{4 x}}{25}+32 x^{3}-\frac {16 x \,{\mathrm e}^{2 x}}{5}+48 x^{2}-\frac {8 \,{\mathrm e}^{2 x}}{5}+27 x +\frac {x \left (2 \ln \relax (x ) {\mathrm e}^{4 x} x^{2}+2 x \,{\mathrm e}^{4 x} \ln \relax (x )-80 x^{2} {\mathrm e}^{2 x} \ln \relax (x )+x \,{\mathrm e}^{4 x}+2 \ln \relax (x ) {\mathrm e}^{4 x}-80 x \,{\mathrm e}^{2 x} \ln \relax (x )+800 x^{2} \ln \relax (x )-40 x \,{\mathrm e}^{2 x}-80 \ln \relax (x ) {\mathrm e}^{2 x}+800 x \ln \relax (x )+400 x +800 \ln \relax (x )\right )}{25 \ln \relax (x )^{2}}\)	\(196\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*(((4*x^4+12*x^3+18*x^2+14*x+6)*exp(x)^4+(-80*x^4-320*x^3-480*x^2-400*x-160)*exp(x)^2+1600*x^3+2400*x^
2+2400*x+675)*ln(x)^3+((8*x^3+14*x^2+12*x+2)*exp(x)^4+(-160*x^3-400*x^2-320*x-80)*exp(x)^2+2400*x^2+1600*x+800
)*ln(x)^2+((2*x^2-2)*exp(x)^4+80*exp(x)^2-800*x^2-800)*ln(x)-2*x*exp(x)^4+80*x*exp(x)^2-800*x)/ln(x)^3,x,metho
d=_RETURNVERBOSE)

[Out]

1/25*x^4*exp(4*x)+2/25*x^3*exp(4*x)-8/5*exp(2*x)*x^4+3/25*x^2*exp(4*x)-16/5*exp(2*x)*x^3+2/25*x*exp(4*x)+16*x^
4-24/5*exp(2*x)*x^2+1/25*exp(4*x)+32*x^3-16/5*x*exp(2*x)+48*x^2-8/5*exp(2*x)+27*x+1/25*x*(2*ln(x)*exp(4*x)*x^2
+2*x*exp(4*x)*ln(x)-80*x^2*exp(2*x)*ln(x)+x*exp(4*x)+2*ln(x)*exp(4*x)-80*x*exp(2*x)*ln(x)+800*x^2*ln(x)-40*x*e
xp(2*x)-80*ln(x)*exp(2*x)+800*x*ln(x)+400*x+800*ln(x))/ln(x)^2

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 16 \, x^{4} + 32 \, x^{3} + 48 \, x^{2} + \frac {1}{800} \, {\left (32 \, x^{4} - 32 \, x^{3} + 24 \, x^{2} - 12 \, x + 3\right )} e^{\left (4 \, x\right )} + \frac {3}{800} \, {\left (32 \, x^{3} - 24 \, x^{2} + 12 \, x - 3\right )} e^{\left (4 \, x\right )} + \frac {9}{400} \, {\left (8 \, x^{2} - 4 \, x + 1\right )} e^{\left (4 \, x\right )} + \frac {7}{200} \, {\left (4 \, x - 1\right )} e^{\left (4 \, x\right )} - \frac {4}{5} \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} - \frac {8}{5} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} - \frac {24}{5} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + 27 \, x + \frac {{\left (x^{2} + 2 \, {\left (x^{3} + x^{2} + x\right )} \log \relax (x)\right )} e^{\left (4 \, x\right )} - 40 \, {\left (x^{2} + 2 \, {\left (x^{3} + x^{2} + x\right )} \log \relax (x)\right )} e^{\left (2 \, x\right )} + 800 \, {\left (x^{3} + x\right )} \log \relax (x)}{25 \, \log \relax (x)^{2}} + \frac {3}{50} \, e^{\left (4 \, x\right )} - \frac {16}{5} \, e^{\left (2 \, x\right )} + 128 \, \Gamma \left (-2, -2 \, \log \relax (x)\right ) + 64 \, \int \frac {x}{\log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((4*x^4+12*x^3+18*x^2+14*x+6)*exp(x)^4+(-80*x^4-320*x^3-480*x^2-400*x-160)*exp(x)^2+1600*x^3+2
400*x^2+2400*x+675)*log(x)^3+((8*x^3+14*x^2+12*x+2)*exp(x)^4+(-160*x^3-400*x^2-320*x-80)*exp(x)^2+2400*x^2+160
0*x+800)*log(x)^2+((2*x^2-2)*exp(x)^4+80*exp(x)^2-800*x^2-800)*log(x)-2*x*exp(x)^4+80*x*exp(x)^2-800*x)/log(x)
^3,x, algorithm="maxima")

[Out]

16*x^4 + 32*x^3 + 48*x^2 + 1/800*(32*x^4 - 32*x^3 + 24*x^2 - 12*x + 3)*e^(4*x) + 3/800*(32*x^3 - 24*x^2 + 12*x
- 3)*e^(4*x) + 9/400*(8*x^2 - 4*x + 1)*e^(4*x) + 7/200*(4*x - 1)*e^(4*x) - 4/5*(2*x^4 - 4*x^3 + 6*x^2 - 6*x +
3)*e^(2*x) - 8/5*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x) - 24/5*(2*x^2 - 2*x + 1)*e^(2*x) - 4*(2*x - 1)*e^(2*x) + 2
7*x + 1/25*((x^2 + 2*(x^3 + x^2 + x)*log(x))*e^(4*x) - 40*(x^2 + 2*(x^3 + x^2 + x)*log(x))*e^(2*x) + 800*(x^3
+ x)*log(x))/log(x)^2 + 3/50*e^(4*x) - 16/5*e^(2*x) + 128*gamma(-2, -2*log(x)) + 64*integrate(x/log(x), x)

________________________________________________________________________________________

mupad [B]  time = 6.21, size = 233, normalized size = 7.28 \begin {gather*} 27\,x-\frac {8\,{\mathrm {e}}^{2\,x}}{5}+\frac {{\mathrm {e}}^{4\,x}}{25}-\frac {16\,x\,{\mathrm {e}}^{2\,x}}{5}+\frac {2\,x\,{\mathrm {e}}^{4\,x}}{25}+\frac {32\,x}{\ln \relax (x)}-\frac {24\,x^2\,{\mathrm {e}}^{2\,x}}{5}-\frac {16\,x^3\,{\mathrm {e}}^{2\,x}}{5}+\frac {3\,x^2\,{\mathrm {e}}^{4\,x}}{25}-\frac {8\,x^4\,{\mathrm {e}}^{2\,x}}{5}+\frac {2\,x^3\,{\mathrm {e}}^{4\,x}}{25}+\frac {x^4\,{\mathrm {e}}^{4\,x}}{25}+\frac {32\,x^2}{\ln \relax (x)}+\frac {16\,x^2}{{\ln \relax (x)}^2}+\frac {32\,x^3}{\ln \relax (x)}+48\,x^2+32\,x^3+16\,x^4-\frac {16\,x\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}+\frac {2\,x\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)}-\frac {16\,x^2\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}-\frac {8\,x^2\,{\mathrm {e}}^{2\,x}}{5\,{\ln \relax (x)}^2}-\frac {16\,x^3\,{\mathrm {e}}^{2\,x}}{5\,\ln \relax (x)}+\frac {2\,x^2\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)}+\frac {x^2\,{\mathrm {e}}^{4\,x}}{25\,{\ln \relax (x)}^2}+\frac {2\,x^3\,{\mathrm {e}}^{4\,x}}{25\,\ln \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((16*x*exp(2*x))/5 - 32*x - (2*x*exp(4*x))/25 + (log(x)^3*(2400*x + exp(4*x)*(14*x + 18*x^2 + 12*x^3 + 4*x
^4 + 6) - exp(2*x)*(400*x + 480*x^2 + 320*x^3 + 80*x^4 + 160) + 2400*x^2 + 1600*x^3 + 675))/25 + (log(x)^2*(16
00*x + exp(4*x)*(12*x + 14*x^2 + 8*x^3 + 2) - exp(2*x)*(320*x + 400*x^2 + 160*x^3 + 80) + 2400*x^2 + 800))/25
+ (log(x)*(80*exp(2*x) + exp(4*x)*(2*x^2 - 2) - 800*x^2 - 800))/25)/log(x)^3,x)

[Out]

27*x - (8*exp(2*x))/5 + exp(4*x)/25 - (16*x*exp(2*x))/5 + (2*x*exp(4*x))/25 + (32*x)/log(x) - (24*x^2*exp(2*x)
)/5 - (16*x^3*exp(2*x))/5 + (3*x^2*exp(4*x))/25 - (8*x^4*exp(2*x))/5 + (2*x^3*exp(4*x))/25 + (x^4*exp(4*x))/25
+ (32*x^2)/log(x) + (16*x^2)/log(x)^2 + (32*x^3)/log(x) + 48*x^2 + 32*x^3 + 16*x^4 - (16*x*exp(2*x))/(5*log(x
)) + (2*x*exp(4*x))/(25*log(x)) - (16*x^2*exp(2*x))/(5*log(x)) - (8*x^2*exp(2*x))/(5*log(x)^2) - (16*x^3*exp(2
*x))/(5*log(x)) + (2*x^2*exp(4*x))/(25*log(x)) + (x^2*exp(4*x))/(25*log(x)^2) + (2*x^3*exp(4*x))/(25*log(x))

________________________________________________________________________________________

sympy [B]  time = 0.55, size = 233, normalized size = 7.28 \begin {gather*} 16 x^{4} + 32 x^{3} + 48 x^{2} + 27 x + \frac {16 x^{2} + \left (32 x^{3} + 32 x^{2} + 32 x\right ) \log {\relax (x )}}{\log {\relax (x )}^{2}} + \frac {\left (- 200 x^{4} \log {\relax (x )}^{4} - 400 x^{3} \log {\relax (x )}^{4} - 400 x^{3} \log {\relax (x )}^{3} - 600 x^{2} \log {\relax (x )}^{4} - 400 x^{2} \log {\relax (x )}^{3} - 200 x^{2} \log {\relax (x )}^{2} - 400 x \log {\relax (x )}^{4} - 400 x \log {\relax (x )}^{3} - 200 \log {\relax (x )}^{4}\right ) e^{2 x} + \left (5 x^{4} \log {\relax (x )}^{4} + 10 x^{3} \log {\relax (x )}^{4} + 10 x^{3} \log {\relax (x )}^{3} + 15 x^{2} \log {\relax (x )}^{4} + 10 x^{2} \log {\relax (x )}^{3} + 5 x^{2} \log {\relax (x )}^{2} + 10 x \log {\relax (x )}^{4} + 10 x \log {\relax (x )}^{3} + 5 \log {\relax (x )}^{4}\right ) e^{4 x}}{125 \log {\relax (x )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((4*x**4+12*x**3+18*x**2+14*x+6)*exp(x)**4+(-80*x**4-320*x**3-480*x**2-400*x-160)*exp(x)**2+16
00*x**3+2400*x**2+2400*x+675)*ln(x)**3+((8*x**3+14*x**2+12*x+2)*exp(x)**4+(-160*x**3-400*x**2-320*x-80)*exp(x)
**2+2400*x**2+1600*x+800)*ln(x)**2+((2*x**2-2)*exp(x)**4+80*exp(x)**2-800*x**2-800)*ln(x)-2*x*exp(x)**4+80*x*e
xp(x)**2-800*x)/ln(x)**3,x)

[Out]

16*x**4 + 32*x**3 + 48*x**2 + 27*x + (16*x**2 + (32*x**3 + 32*x**2 + 32*x)*log(x))/log(x)**2 + ((-200*x**4*log
(x)**4 - 400*x**3*log(x)**4 - 400*x**3*log(x)**3 - 600*x**2*log(x)**4 - 400*x**2*log(x)**3 - 200*x**2*log(x)**
2 - 400*x*log(x)**4 - 400*x*log(x)**3 - 200*log(x)**4)*exp(2*x) + (5*x**4*log(x)**4 + 10*x**3*log(x)**4 + 10*x
**3*log(x)**3 + 15*x**2*log(x)**4 + 10*x**2*log(x)**3 + 5*x**2*log(x)**2 + 10*x*log(x)**4 + 10*x*log(x)**3 + 5
*log(x)**4)*exp(4*x))/(125*log(x)**4)

________________________________________________________________________________________