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

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

________________________________________________________________________________________

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

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

________________________________________________________________________________________

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

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 $$\begin{array}{c}\frac{x^2{e}^{\left(4x\right)}-40x^2{e}^{\left(2x\right)}+(400x^4+800x^3+1200x^2+(x^4+2x^3+3x^2+2x+1)e^{\left(4x\right)}-40(x^4+2x^3+3x^2+2x+1)e^{\left(2x\right)}+675x)\log (x{)}^2+400x^2+2(400x^3+400x^2+(x^3+x^2+x)e^{\left(4x\right)}-40(x^3+x^2+x)e^{\left(2x\right)}+400x)\log (x)}{25\log (x{)}^2}\end{array}$$

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 $$\begin{array}{c}16x^4+32x^3+48x^2+\frac{1}{800}(32x^4-32x^3+24x^2-12x+3)e^{\left(4x\right)}+\frac{3}{800}(32x^3-24x^2+12x-3)e^{\left(4x\right)}+\frac{9}{400}(8x^2-4x+1)e^{\left(4x\right)}+\frac{7}{200}(4x-1)e^{\left(4x\right)}-\frac{4}{5}(2x^4-4x^3+6x^2-6x+3)e^{\left(2x\right)}-\frac{8}{5}(4x^3-6x^2+6x-3)e^{\left(2x\right)}-\frac{24}{5}(2x^2-2x+1)e^{\left(2x\right)}-4(2x-1)e^{\left(2x\right)}+27x+\frac{2x^3{e}^{\left(4x\right)}\log (x)-80x^3{e}^{\left(2x\right)}\log (x)+2x^2{e}^{\left(4x\right)}\log (x)-80x^2{e}^{\left(2x\right)}\log (x)+x^2{e}^{\left(4x\right)}-40x^2{e}^{\left(2x\right)}+2x{e}^{\left(4x\right)}\log (x)-80x{e}^{\left(2x\right)}\log (x)}{25\log (x{)}^2}+\frac{16(2x^3\log (x)+2x^2\log (x)+x^2+2x\log (x))}{\log (x{)}^2}+\frac{3}{50}{e}^{\left(4x\right)}-\frac{16}{5}{e}^{\left(2x\right)}\end{array}$$

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	$\frac{x^4{\mathrm{e}}^{4x}}{25}+\frac{2x^3{\mathrm{e}}^{4x}}{25}-\frac{8{\mathrm{e}}^{2x}{x}^4}{5}+\frac{3x^2{\mathrm{e}}^{4x}}{25}-\frac{16{\mathrm{e}}^{2x}{x}^3}{5}+\frac{2x{\mathrm{e}}^{4x}}{25}+16x^4-\frac{24{\mathrm{e}}^{2x}{x}^2}{5}+\frac{{\mathrm{e}}^{4x}}{25}+32x^3-\frac{16x{\mathrm{e}}^{2x}}{5}+48x^2-\frac{8{\mathrm{e}}^{2x}}{5}+27x+\frac{x(2\ln (x){\mathrm{e}}^{4x}{x}^2+2x{\mathrm{e}}^{4x}\ln (x)-80x^2{\mathrm{e}}^{2x}\ln (x)+x{\mathrm{e}}^{4x}+2\ln (x){\mathrm{e}}^{4x}-80x{\mathrm{e}}^{2x}\ln (x)+800x^2\ln (x)-40x{\mathrm{e}}^{2x}-80\ln (x){\mathrm{e}}^{2x}+800x\ln (x)+400x+800\ln (x))}{25\ln (x{)}^2}$	$196$

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 $$\begin{array}{c}16x^4+32x^3+48x^2+\frac{1}{800}(32x^4-32x^3+24x^2-12x+3)e^{\left(4x\right)}+\frac{3}{800}(32x^3-24x^2+12x-3)e^{\left(4x\right)}+\frac{9}{400}(8x^2-4x+1)e^{\left(4x\right)}+\frac{7}{200}(4x-1)e^{\left(4x\right)}-\frac{4}{5}(2x^4-4x^3+6x^2-6x+3)e^{\left(2x\right)}-\frac{8}{5}(4x^3-6x^2+6x-3)e^{\left(2x\right)}-\frac{24}{5}(2x^2-2x+1)e^{\left(2x\right)}-4(2x-1)e^{\left(2x\right)}+27x+\frac{(x^2+2(x^3+x^2+x)\log (x))e^{\left(4x\right)}-40(x^2+2(x^3+x^2+x)\log (x))e^{\left(2x\right)}+800(x^3+x)\log (x)}{25\log (x{)}^2}+\frac{3}{50}{e}^{\left(4x\right)}-\frac{16}{5}{e}^{\left(2x\right)}+128\mathrm{\Gamma }(-2,-2\log (x))+64\int \frac{x}{\log (x)}dx\end{array}$$

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 $$\begin{array}{c}27x-\frac{8{\mathrm{e}}^{2x}}{5}+\frac{{\mathrm{e}}^{4x}}{25}-\frac{16x{\mathrm{e}}^{2x}}{5}+\frac{2x{\mathrm{e}}^{4x}}{25}+\frac{32x}{\ln (x)}-\frac{24x^2{\mathrm{e}}^{2x}}{5}-\frac{16x^3{\mathrm{e}}^{2x}}{5}+\frac{3x^2{\mathrm{e}}^{4x}}{25}-\frac{8x^4{\mathrm{e}}^{2x}}{5}+\frac{2x^3{\mathrm{e}}^{4x}}{25}+\frac{x^4{\mathrm{e}}^{4x}}{25}+\frac{32x^2}{\ln (x)}+\frac{16x^2}{{\ln (x)}^2}+\frac{32x^3}{\ln (x)}+48x^2+32x^3+16x^4-\frac{16x{\mathrm{e}}^{2x}}{5\ln (x)}+\frac{2x{\mathrm{e}}^{4x}}{25\ln (x)}-\frac{16x^2{\mathrm{e}}^{2x}}{5\ln (x)}-\frac{8x^2{\mathrm{e}}^{2x}}{5{\ln (x)}^2}-\frac{16x^3{\mathrm{e}}^{2x}}{5\ln (x)}+\frac{2x^2{\mathrm{e}}^{4x}}{25\ln (x)}+\frac{x^2{\mathrm{e}}^{4x}}{25{\ln (x)}^2}+\frac{2x^3{\mathrm{e}}^{4x}}{25\ln (x)}\end{array}$$

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 $$\begin{array}{c}16x^4+32x^3+48x^2+27x+\frac{16x^2+(32x^3+32x^2+32x)\log (x)}{\log {(x)}^2}+\frac{(-200x^4\log {(x)}^4-400x^3\log {(x)}^4-400x^3\log {(x)}^3-600x^2\log {(x)}^4-400x^2\log {(x)}^3-200x^2\log {(x)}^2-400x\log {(x)}^4-400x\log {(x)}^3-200\log {(x)}^4)e^{2x}+(5x^4\log {(x)}^4+10x^3\log {(x)}^4+10x^3\log {(x)}^3+15x^2\log {(x)}^4+10x^2\log {(x)}^3+5x^2\log {(x)}^2+10x\log {(x)}^4+10x\log {(x)}^3+5\log {(x)}^4)e^{4x}}{125\log {(x)}^4}\end{array}$$

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)

________________________________________________________________________________________