3.17.11 $\int \frac{-2x^2\log (x)\log (\frac{5e^x\log (x)}{x})+e^{10}{\log }^2(\frac{5e^x\log (x)}{x})(-32-16x-2x^2+(32-16x-14x^2-2x^3)\log (x)+(-8x-2x^2)\log (x)\log (\frac{5e^x\log (x)}{x}))+e^5\log (\frac{5e^x\log (x)}{x})(8x+2x^2+(-8x+6x^2+2x^3)\log (x)+(8x+4x^2)\log (x)\log (\frac{5e^x\log (x)}{x}))}{x\log (x)\log (\frac{5e^x\log (x)}{x})}dx$

Optimal. Leaf size=28 $$3-{(-x+e^5(4+x)\log \left(\frac{5e^x\log (x)}{x}\right))}^2$$

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Rubi [F]  time = 2.53, 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 = {} $$\begin{array}{c}\int \frac{-2x^2\log (x)\log \left(\frac{5e^x\log (x)}{x}\right)+e^{10}{\log }^2\left(\frac{5e^x\log (x)}{x}\right)(-32-16x-2x^2+(32-16x-14x^2-2x^3)\log (x)+(-8x-2x^2)\log (x)\log \left(\frac{5e^x\log (x)}{x}\right))+e^5\log \left(\frac{5e^x\log (x)}{x}\right)(8x+2x^2+(-8x+6x^2+2x^3)\log (x)+(8x+4x^2)\log (x)\log \left(\frac{5e^x\log (x)}{x}\right))}{x\log (x)\log \left(\frac{5e^x\log (x)}{x}\right)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-2*x^2*Log[x]*Log[(5*E^x*Log[x])/x] + E^10*Log[(5*E^x*Log[x])/x]^2*(-32 - 16*x - 2*x^2 + (32 - 16*x - 14*
x^2 - 2*x^3)*Log[x] + (-8*x - 2*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]) + E^5*Log[(5*E^x*Log[x])/x]*(8*x + 2*x^2 +
(-8*x + 6*x^2 + 2*x^3)*Log[x] + (8*x + 4*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]))/(x*Log[x]*Log[(5*E^x*Log[x])/x]),
x]

[Out]

-8*E^5*x + 16*E^10*x + 8*E^5*(1 - 2*E^5)*x - x^2 + 3*E^5*x^2 + (E^5*(2 - 7*E^5)*x^2)/2 - 4*E^5*(1 - 2*E^5)*x^2
+ (2*E^5*x^3)/3 - (2*E^10*x^3)/9 - (E^5*(2 - 7*E^5)*x^3)/3 + (E^10*x^4)/6 + 2*E^5*ExpIntegralEi[2*Log[x]] - 1
6*E^10*ExpIntegralEi[2*Log[x]] - E^5*(2 - 7*E^5)*ExpIntegralEi[2*Log[x]] + (2*E^10*ExpIntegralEi[3*Log[x]])/3
+ 8*E^5*(1 - 2*E^5)*x*Log[(5*E^x*Log[x])/x] + E^5*(2 - 7*E^5)*x^2*Log[(5*E^x*Log[x])/x] - (2*E^10*x^3*Log[(5*E
^x*Log[x])/x])/3 + 8*E^5*LogIntegral[x] - 8*E^5*(1 - 2*E^5)*LogIntegral[x] + 16*E^10*x*LogIntegral[x] - 16*E^1
0*Log[x]*LogIntegral[x] - 16*E^10*Log[(5*E^x*Log[x])/x]*LogIntegral[x] + 32*E^10*Defer[Int][Log[(5*E^x*Log[x])
/x]/x, x] - 32*E^10*Defer[Int][Log[(5*E^x*Log[x])/x]/(x*Log[x]), x] - 2*E^10*Defer[Int][(x*Log[(5*E^x*Log[x])/
x])/Log[x], x] - 8*E^10*Defer[Int][Log[(5*E^x*Log[x])/x]^2, x] - 2*E^10*Defer[Int][x*Log[(5*E^x*Log[x])/x]^2,
x] + 16*E^10*Defer[Int][LogIntegral[x]/(x*Log[x]), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{2(x-e^5(4+x)\log \left(\frac{5e^x\log (x)}{x}\right))(e^5(4+x)+\log (x)(-x+e^5(-4+3x+x^2)+e^{5}x\log \left(\frac{5e^x\log (x)}{x}\right)))}{x\log (x)}dx\\ & =2\int \frac{(x-e^5(4+x)\log \left(\frac{5e^x\log (x)}{x}\right))(e^5(4+x)+\log (x)(-x+e^5(-4+3x+x^2)+e^{5}x\log \left(\frac{5e^x\log (x)}{x}\right)))}{x\log (x)}dx\\ & =2\int (\frac{4e^5+e^{5}x-4e^5\log (x)-(1-3e^5)x\log (x)+e^5{x}^2\log (x)}{\log (x)}+\frac{e^5(-16e^5-8e^{5}x-e^5{x}^2+16e^5\log (x)+4(1-2e^5)x\log (x)+2(1-\frac{7e^5}{2})x^2\log (x)-e^5{x}^3\log (x))\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}-e^{10}(4+x){\log }^2\left(\frac{5e^x\log (x)}{x}\right))dx\\ & =2\int \frac{4e^5+e^{5}x-4e^5\log (x)-(1-3e^5)x\log (x)+e^5{x}^2\log (x)}{\log (x)}dx+\left(2e^5\right)\int \frac{(-16e^5-8e^{5}x-e^5{x}^2+16e^5\log (x)+4(1-2e^5)x\log (x)+2(1-\frac{7e^5}{2})x^2\log (x)-e^5{x}^3\log (x))\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(2e^{10}\right)\int (4+x){\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx\\ & =2\int (-x+e^5(-4+3x+x^2)+\frac{e^5(4+x)}{\log (x)})dx+\left(2e^5\right)\int \frac{(-e^5(4+x{)}^2-(-2x(2+x)+e^5(-1+x)(4+x{)}^2)\log (x))\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(2e^{10}\right)\int (4{\log }^2\left(\frac{5e^x\log (x)}{x}\right)+x{\log }^2\left(\frac{5e^x\log (x)}{x}\right))dx\\ & =-x^2+\left(2e^5\right)\int (-4+3x+x^2)dx+\left(2e^5\right)\int \frac{4+x}{\log (x)}dx+\left(2e^5\right)\int (4(1-2e^5)\log \left(\frac{5e^x\log (x)}{x}\right)+\frac{16e^5\log \left(\frac{5e^x\log (x)}{x}\right)}{x}+2(1-\frac{7e^5}{2})x\log \left(\frac{5e^x\log (x)}{x}\right)-e^5{x}^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{8e^5\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}-\frac{16e^5\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}-\frac{e^{5}x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)})dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx\\ & =-8e^{5}x-x^2+3e^5{x}^2+\frac{2e^5{x}^3}{3}+\left(2e^5\right)\int (\frac{4}{\log (x)}+\frac{x}{\log (x)})dx-\left(2e^{10}\right)\int x^2\log \left(\frac{5e^x\log (x)}{x}\right)dx-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(16e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx+\left(2e^5(2-7e^5)\right)\int x\log \left(\frac{5e^x\log (x)}{x}\right)dx+\left(8e^5(1-2e^5)\right)\int \log \left(\frac{5e^x\log (x)}{x}\right)dx\\ & =-8e^{5}x-x^2+3e^5{x}^2+\frac{2e^5{x}^3}{3}+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)+\left(2e^5\right)\int \frac{x}{\log (x)}dx+\left(8e^5\right)\int \frac{1}{\log (x)}dx+\left(2e^{10}\right)\int \frac{x^2(1+(-1+x)\log (x))}{3\log (x)}dx-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \frac{(1+(-1+x)\log (x))\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(2e^5(2-7e^5)\right)\int \frac{x(1+(-1+x)\log (x))}{2\log (x)}dx-\left(8e^5(1-2e^5)\right)\int (-1+x+\frac{1}{\log (x)})dx\\ & =-8e^{5}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)+\left(2e^5\right)\mathrm{Subst}(\int \frac{e^{2x}}{x}dx,x,\log (x))+\frac{1}{3}\left(2e^{10}\right)\int \frac{x^2(1+(-1+x)\log (x))}{\log (x)}dx-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int (\text{li}(x)-\frac{\text{li}(x)}{x}+\frac{\text{li}(x)}{x\log (x)})dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(e^5(2-7e^5)\right)\int \frac{x(1+(-1+x)\log (x))}{\log (x)}dx-\left(8e^5(1-2e^5)\right)\int \frac{1}{\log (x)}dx\\ & =-8e^{5}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}+2e^5\text{Ei}(2\log (x))+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-8e^5(1-2e^5)\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)+\frac{1}{3}\left(2e^{10}\right)\int ((-1+x)x^2+\frac{x^2}{\log (x)})dx-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \text{li}(x)dx-\left(16e^{10}\right)\int \frac{\text{li}(x)}{x}dx+\left(16e^{10}\right)\int \frac{\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(e^5(2-7e^5)\right)\int x(-1+x+\frac{1}{\log (x)})dx\\ & =-8e^{5}x+16e^{10}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}+2e^5\text{Ei}(2\log (x))-16e^{10}\text{Ei}(2\log (x))+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-8e^5(1-2e^5)\text{li}(x)+16e^{10}x\text{li}(x)-16e^{10}\log (x)\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)+\frac{1}{3}\left(2e^{10}\right)\int (-1+x)x^{2}dx+\frac{1}{3}\left(2e^{10}\right)\int \frac{x^2}{\log (x)}dx-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \frac{\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(e^5(2-7e^5)\right)\int ((-1+x)x+\frac{x}{\log (x)})dx\\ & =-8e^{5}x+16e^{10}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}+2e^5\text{Ei}(2\log (x))-16e^{10}\text{Ei}(2\log (x))+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-8e^5(1-2e^5)\text{li}(x)+16e^{10}x\text{li}(x)-16e^{10}\log (x)\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)+\frac{1}{3}\left(2e^{10}\right)\int (-x^2+x^3)dx+\frac{1}{3}\left(2e^{10}\right)\mathrm{Subst}(\int \frac{e^{3x}}{x}dx,x,\log (x))-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \frac{\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(e^5(2-7e^5)\right)\int (-1+x)xdx-\left(e^5(2-7e^5)\right)\int \frac{x}{\log (x)}dx\\ & =-8e^{5}x+16e^{10}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}-\frac{2e^{10}{x}^3}{9}+\frac{e^{10}{x}^4}{6}+2e^5\text{Ei}(2\log (x))-16e^{10}\text{Ei}(2\log (x))+\frac{2}{3}{e}^{10}\text{Ei}(3\log (x))+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-8e^5(1-2e^5)\text{li}(x)+16e^{10}x\text{li}(x)-16e^{10}\log (x)\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \frac{\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx-\left(e^5(2-7e^5)\right)\int (-x+x^2)dx-\left(e^5(2-7e^5)\right)\mathrm{Subst}(\int \frac{e^{2x}}{x}dx,x,\log (x))\\ & =-8e^{5}x+16e^{10}x+8e^5(1-2e^5)x-x^2+3e^5{x}^2+\frac{1}{2}{e}^5(2-7e^5)x^2-4e^5(1-2e^5)x^2+\frac{2e^5{x}^3}{3}-\frac{2e^{10}{x}^3}{9}-\frac{1}{3}{e}^5(2-7e^5)x^3+\frac{e^{10}{x}^4}{6}+2e^5\text{Ei}(2\log (x))-16e^{10}\text{Ei}(2\log (x))-e^5(2-7e^5)\text{Ei}(2\log (x))+\frac{2}{3}{e}^{10}\text{Ei}(3\log (x))+8e^5(1-2e^5)x\log \left(\frac{5e^x\log (x)}{x}\right)+e^5(2-7e^5)x^2\log \left(\frac{5e^x\log (x)}{x}\right)-\frac{2}{3}{e}^{10}{x}^3\log \left(\frac{5e^x\log (x)}{x}\right)+8e^5\text{li}(x)-8e^5(1-2e^5)\text{li}(x)+16e^{10}x\text{li}(x)-16e^{10}\log (x)\text{li}(x)-16e^{10}\log \left(\frac{5e^x\log (x)}{x}\right)\text{li}(x)-\left(2e^{10}\right)\int \frac{x\log \left(\frac{5e^x\log (x)}{x}\right)}{\log (x)}dx-\left(2e^{10}\right)\int x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx-\left(8e^{10}\right)\int {\log }^2\left(\frac{5e^x\log (x)}{x}\right)dx+\left(16e^{10}\right)\int \frac{\text{li}(x)}{x\log (x)}dx+\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x}dx-\left(32e^{10}\right)\int \frac{\log \left(\frac{5e^x\log (x)}{x}\right)}{x\log (x)}dx\end{array}\end{array}$$

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Mathematica [B]  time = 0.45, size = 180, normalized size = 6.43 $$\begin{array}{c}-x^2+16e^{10}{x}^2-16e^{10}{\log }^2\left(\frac{\log (x)}{x}\right)-32e^{10}\log (x)(x+\log \left(\frac{\log (x)}{x}\right)-\log \left(\frac{5e^x\log (x)}{x}\right))+32e^{10}\log (\log (x))(x+\log \left(\frac{\log (x)}{x}\right)-\log \left(\frac{5e^x\log (x)}{x}\right))+8e^{5}x\log \left(\frac{5e^x\log (x)}{x}\right)-32e^{10}x\log \left(\frac{5e^x\log (x)}{x}\right)+2e^5{x}^2\log \left(\frac{5e^x\log (x)}{x}\right)-8e^{10}x{\log }^2\left(\frac{5e^x\log (x)}{x}\right)-e^{10}{x}^2{\log }^2\left(\frac{5e^x\log (x)}{x}\right)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^2*Log[x]*Log[(5*E^x*Log[x])/x] + E^10*Log[(5*E^x*Log[x])/x]^2*(-32 - 16*x - 2*x^2 + (32 - 16*x
- 14*x^2 - 2*x^3)*Log[x] + (-8*x - 2*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]) + E^5*Log[(5*E^x*Log[x])/x]*(8*x + 2*
x^2 + (-8*x + 6*x^2 + 2*x^3)*Log[x] + (8*x + 4*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]))/(x*Log[x]*Log[(5*E^x*Log[x]
)/x]),x]

[Out]

-x^2 + 16*E^10*x^2 - 16*E^10*Log[Log[x]/x]^2 - 32*E^10*Log[x]*(x + Log[Log[x]/x] - Log[(5*E^x*Log[x])/x]) + 32
*E^10*Log[Log[x]]*(x + Log[Log[x]/x] - Log[(5*E^x*Log[x])/x]) + 8*E^5*x*Log[(5*E^x*Log[x])/x] - 32*E^10*x*Log[
(5*E^x*Log[x])/x] + 2*E^5*x^2*Log[(5*E^x*Log[x])/x] - 8*E^10*x*Log[(5*E^x*Log[x])/x]^2 - E^10*x^2*Log[(5*E^x*L
og[x])/x]^2

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fricas [A]  time = 0.73, size = 51, normalized size = 1.82 $$\begin{array}{c}-(x^2+8x+16)e^{10}\log {\left(\frac{5e^x\log (x)}{x}\right)}^2+2(x^2+4x)e^5\log \left(\frac{5e^x\log (x)}{x}\right)-x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="fricas")

[Out]

-(x^2 + 8*x + 16)*e^10*log(5*e^x*log(x)/x)^2 + 2*(x^2 + 4*x)*e^5*log(5*e^x*log(x)/x) - x^2

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giac [B]  time = 0.38, size = 338, normalized size = 12.07 $$\begin{array}{c}-x^4{e}^{10}-2x^3{e}^{10}\log (5)-x^2{e}^{10}\log (5{)}^2+2x^3{e}^{10}\log (x)+2x^2{e}^{10}\log (5)\log (x)-x^2{e}^{10}\log (x{)}^2-2x^3{e}^{10}\log (\log (x))-2x^2{e}^{10}\log (5)\log (\log (x))+2x^2{e}^{10}\log (x)\log (\log (x))-x^2{e}^{10}\log {(\log (x))}^2-8x^3{e}^{10}+2x^3{e}^5-16x^2{e}^{10}\log (5)+2x^2{e}^5\log (5)-8x{e}^{10}\log (5{)}^2+16x^2{e}^{10}\log (x)-2x^2{e}^5\log (x)+16x{e}^{10}\log (5)\log (x)-8x{e}^{10}\log (x{)}^2-16x^2{e}^{10}\log (\log (x))+2x^2{e}^5\log (\log (x))-16x{e}^{10}\log (5)\log (\log (x))+16x{e}^{10}\log (x)\log (\log (x))-8x{e}^{10}\log {(\log (x))}^2-16x^2{e}^{10}+8x^2{e}^5-32x{e}^{10}\log (5)+8x{e}^5\log (5)+32x{e}^{10}\log (x)-8x{e}^5\log (x)+32e^{10}\log (5)\log (x)-16e^{10}\log (x{)}^2-32x{e}^{10}\log (\log (x))+8x{e}^5\log (\log (x))-32e^{10}\log (5)\log (\log (x))+32e^{10}\log (x)\log (\log (x))-16e^{10}\log {(\log (x))}^2-x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="giac")

[Out]

-x^4*e^10 - 2*x^3*e^10*log(5) - x^2*e^10*log(5)^2 + 2*x^3*e^10*log(x) + 2*x^2*e^10*log(5)*log(x) - x^2*e^10*lo
g(x)^2 - 2*x^3*e^10*log(log(x)) - 2*x^2*e^10*log(5)*log(log(x)) + 2*x^2*e^10*log(x)*log(log(x)) - x^2*e^10*log
(log(x))^2 - 8*x^3*e^10 + 2*x^3*e^5 - 16*x^2*e^10*log(5) + 2*x^2*e^5*log(5) - 8*x*e^10*log(5)^2 + 16*x^2*e^10*
log(x) - 2*x^2*e^5*log(x) + 16*x*e^10*log(5)*log(x) - 8*x*e^10*log(x)^2 - 16*x^2*e^10*log(log(x)) + 2*x^2*e^5*
log(log(x)) - 16*x*e^10*log(5)*log(log(x)) + 16*x*e^10*log(x)*log(log(x)) - 8*x*e^10*log(log(x))^2 - 16*x^2*e^
10 + 8*x^2*e^5 - 32*x*e^10*log(5) + 8*x*e^5*log(5) + 32*x*e^10*log(x) - 8*x*e^5*log(x) + 32*e^10*log(5)*log(x)
- 16*e^10*log(x)^2 - 32*x*e^10*log(log(x)) + 8*x*e^5*log(log(x)) - 32*e^10*log(5)*log(log(x)) + 32*e^10*log(x
)*log(log(x)) - 16*e^10*log(log(x))^2 - x^2

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maple [C]  time = 1.56, size = 5540, normalized size = 197.86

method	result	size
risch	$\text{Expression too large to display}$	$5540$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^2-8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(-2*x^3-14*x^2-16*x+32)*ln(x)-2*x^2-16*x-32)*exp(ln(ln(5*exp(x)*
ln(x)/x))+5)^2+((4*x^2+8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(2*x^3+6*x^2-8*x)*ln(x)+2*x^2+8*x)*exp(ln(ln(5*exp(x)*l
n(x)/x))+5)-2*x^2*ln(x)*ln(5*exp(x)*ln(x)/x))/x/ln(x)/ln(5*exp(x)*ln(x)/x),x,method=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}-x^4{e}^{10}-\frac{2}{3}(3(\log (5)+4)e^{10}-2e^5)x^3+\frac{2}{3}{x}^3{e}^5-((\log (5{)}^2+16\log (5)+16)e^{10}-(2\log (5)+5)e^5)x^2+3x^2{e}^5-(x^2{e}^{10}+8x{e}^{10}+16e^{10})\log (x{)}^2-(x^2{e}^{10}+8x{e}^{10}+16e^{10})\log {(\log (x))}^2-8((\log (5{)}^2+4\log (5))e^{10}-(\log (5)+1)e^5)x-x^2-8x{e}^5+2\mathrm{E}\mathrm{i}(2\log (x))e^5+8\mathrm{E}\mathrm{i}(\log (x))e^5+2(x^3{e}^{10}+((\log (5)+8)e^{10}-e^5)x^2+4(2(\log (5)+2)e^{10}-e^5)x+16e^{10}\log (5))\log (x)-2(x^3{e}^{10}+((\log (5)+8)e^{10}-e^5)x^2+4(2(\log (5)+2)e^{10}-e^5)x-(x^2{e}^{10}+8x{e}^{10}+16e^{10})\log (x))\log (\log (x))-2\int \frac{x^2{e}^5+4x{e}^5+16e^{10}\log (5)}{x\log (x)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="maxima")

[Out]

-x^4*e^10 - 2/3*(3*(log(5) + 4)*e^10 - 2*e^5)*x^3 + 2/3*x^3*e^5 - ((log(5)^2 + 16*log(5) + 16)*e^10 - (2*log(5
) + 5)*e^5)*x^2 + 3*x^2*e^5 - (x^2*e^10 + 8*x*e^10 + 16*e^10)*log(x)^2 - (x^2*e^10 + 8*x*e^10 + 16*e^10)*log(l
og(x))^2 - 8*((log(5)^2 + 4*log(5))*e^10 - (log(5) + 1)*e^5)*x - x^2 - 8*x*e^5 + 2*Ei(2*log(x))*e^5 + 8*Ei(log
(x))*e^5 + 2*(x^3*e^10 + ((log(5) + 8)*e^10 - e^5)*x^2 + 4*(2*(log(5) + 2)*e^10 - e^5)*x + 16*e^10*log(5))*log
(x) - 2*(x^3*e^10 + ((log(5) + 8)*e^10 - e^5)*x^2 + 4*(2*(log(5) + 2)*e^10 - e^5)*x - (x^2*e^10 + 8*x*e^10 + 1
6*e^10)*log(x))*log(log(x)) - 2*integrate((x^2*e^5 + 4*x*e^5 + 16*e^10*log(5))/(x*log(x)), x)

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mupad [B]  time = 1.59, size = 36, normalized size = 1.29 $$\begin{array}{c}-{(4\ln \left(\frac{5{\mathrm{e}}^x\ln (x)}{x}\right){\mathrm{e}}^5-x+x\ln \left(\frac{5{\mathrm{e}}^x\ln (x)}{x}\right){\mathrm{e}}^5)}^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*log(log((5*exp(x)*log(x))/x)) + 10)*(16*x + 2*x^2 + log(x)*(16*x + 14*x^2 + 2*x^3 - 32) + log((5*e
xp(x)*log(x))/x)*log(x)*(8*x + 2*x^2) + 32) - exp(log(log((5*exp(x)*log(x))/x)) + 5)*(8*x + 2*x^2 + log(x)*(6*
x^2 - 8*x + 2*x^3) + log((5*exp(x)*log(x))/x)*log(x)*(8*x + 4*x^2)) + 2*x^2*log((5*exp(x)*log(x))/x)*log(x))/(
x*log((5*exp(x)*log(x))/x)*log(x)),x)

[Out]

-(4*log((5*exp(x)*log(x))/x)*exp(5) - x + x*log((5*exp(x)*log(x))/x)*exp(5))^2

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sympy [B]  time = 0.78, size = 63, normalized size = 2.25 $$\begin{array}{c}-x^2+(2x^2{e}^5+8x{e}^5)\log \left(\frac{5e^x\log (x)}{x}\right)+(-x^2{e}^{10}-8x{e}^{10}-16e^{10})\log {\left(\frac{5e^x\log (x)}{x}\right)}^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**2-8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(-2*x**3-14*x**2-16*x+32)*ln(x)-2*x**2-16*x-32)*exp(ln(ln
(5*exp(x)*ln(x)/x))+5)**2+((4*x**2+8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(2*x**3+6*x**2-8*x)*ln(x)+2*x**2+8*x)*exp(l
n(ln(5*exp(x)*ln(x)/x))+5)-2*x**2*ln(x)*ln(5*exp(x)*ln(x)/x))/x/ln(x)/ln(5*exp(x)*ln(x)/x),x)

[Out]

-x**2 + (2*x**2*exp(5) + 8*x*exp(5))*log(5*exp(x)*log(x)/x) + (-x**2*exp(10) - 8*x*exp(10) - 16*exp(10))*log(5
*exp(x)*log(x)/x)**2

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