3.17.28 $\int \frac{-54x-6e^{6}x+162x^2-108x^3+e^3(-36x+54x^2)+2^{60/x}{x}^{60/x}(2x-6x^2+4x^3)+2^{20/x}{x}^{20/x}(54x-162x^2+108x^3+e^6(-40+2x)+e^3(-120+144x-36x^2)+(40e^6+e^3(120-120x))\log (2x))+2^{40/x}{x}^{40/x}(-18x+54x^2-36x^3+e^3(40-44x+6x^2)+e^3(-40+40x)\log (2x))}{-27+272^{20/x}{x}^{20/x}-92^{40/x}{x}^{40/x}+2^{60/x}{x}^{60/x}}dx$

Optimal. Leaf size=35 $$x^2{(1-x+\frac{e^3}{3-2^{20/x}{x}^{20/x}})}^2$$

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Rubi [F]  time = 2.98, 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 = {} $$\begin{array}{c}\int \frac{-54x-6e^{6}x+162x^2-108x^3+e^3(-36x+54x^2)+2^{60/x}{x}^{60/x}(2x-6x^2+4x^3)+2^{20/x}{x}^{20/x}(54x-162x^2+108x^3+e^6(-40+2x)+e^3(-120+144x-36x^2)+(40e^6+e^3(120-120x))\log (2x))+2^{40/x}{x}^{40/x}(-18x+54x^2-36x^3+e^3(40-44x+6x^2)+e^3(-40+40x)\log (2x))}{-27+272^{20/x}{x}^{20/x}-92^{40/x}{x}^{40/x}+2^{60/x}{x}^{60/x}}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^(60/x)*x^(60/x)*(2*x - 6*x^2 + 4*x^3) + 2^
(20/x)*x^(20/x)*(54*x - 162*x^2 + 108*x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^3*(120
- 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^3*(40 - 44*x + 6*x^2) + E^3*(-40 + 40*x)
*Log[2*x]))/(-27 + 27*2^(20/x)*x^(20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/x)),x]

[Out]

x^2 - 2*x^3 + x^4 - 120*E^6*Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-3), x] + 120*E^6*Log[2*x]*Defer[Int][(-3 + 2
^(20/x)*x^(20/x))^(-3), x] + 40*E^3*(3 - E^3)*Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-2), x] - 40*E^3*(3 - E^3)*
Log[2*x]*Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-2), x] - 2*E^3*(60 - E^3)*Defer[Int][x/(-3 + 2^(20/x)*x^(20/x))
^2, x] + 120*E^3*Log[2*x]*Defer[Int][x/(-3 + 2^(20/x)*x^(20/x))^2, x] + 40*E^3*Defer[Int][(-3 + 2^(20/x)*x^(20
/x))^(-1), x] - 40*E^3*Log[2*x]*Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-1), x] - 44*E^3*Defer[Int][x/(-3 + 2^(20
/x)*x^(20/x)), x] + 40*E^3*Log[2*x]*Defer[Int][x/(-3 + 2^(20/x)*x^(20/x)), x] + 6*E^3*Defer[Int][x^2/(-3 + 2^(
20/x)*x^(20/x)), x] - 120*E^6*Defer[Int][Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-3), x]/x, x] + 40*E^3*(3 - E^3)
*Defer[Int][Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-2), x]/x, x] - 120*E^3*Defer[Int][Defer[Int][x/(-3 + 2^(20/x
)*x^(20/x))^2, x]/x, x] + 40*E^3*Defer[Int][Defer[Int][(-3 + 2^(20/x)*x^(20/x))^(-1), x]/x, x] - 40*E^3*Defer[
Int][Defer[Int][x/(-3 + 2^(20/x)*x^(20/x)), x]/x, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{(-54-6e^6)x+162x^2-108x^3+e^3(-36x+54x^2)+2^{60/x}{x}^{60/x}(2x-6x^2+4x^3)+2^{20/x}{x}^{20/x}(54x-162x^2+108x^3+e^6(-40+2x)+e^3(-120+144x-36x^2)+(40e^6+e^3(120-120x))\log (2x))+2^{40/x}{x}^{40/x}(-18x+54x^2-36x^3+e^3(40-44x+6x^2)+e^3(-40+40x)\log (2x))}{-27+272^{20/x}{x}^{20/x}-92^{40/x}{x}^{40/x}+2^{60/x}{x}^{60/x}}dx\\ & =\int \frac{-\left((-54-6e^6)x\right)-162x^2+108x^3-e^3(-36x+54x^2)-2^{60/x}{x}^{60/x}(2x-6x^2+4x^3)-2^{20/x}{x}^{20/x}(54x-162x^2+108x^3+e^6(-40+2x)+e^3(-120+144x-36x^2)+(40e^6+e^3(120-120x))\log (2x))-2^{40/x}{x}^{40/x}(-18x+54x^2-36x^3+e^3(40-44x+6x^2)+e^3(-40+40x)\log (2x))}{{(3-2^{20/x}{x}^{20/x})}^3}dx\\ & =\int (2x(1-3x+2x^2)+\frac{120e^6(-1+\log (2x))}{{(-3+2^{20/x}{x}^{20/x})}^3}+\frac{2e^3(20-22x+3x^2-20\log (2x)+20x\log (2x))}{-3+2^{20/x}{x}^{20/x}}+\frac{2e^3(60(1-\frac{e^3}{3})-60(1-\frac{e^3}{60})x-60(1-\frac{e^3}{3})\log (2x)+60x\log (2x))}{{(3-2^{20/x}{x}^{20/x})}^2})dx\\ & =2\int x(1-3x+2x^2)dx+\left(2e^3\right)\int \frac{20-22x+3x^2-20\log (2x)+20x\log (2x)}{-3+2^{20/x}{x}^{20/x}}dx+\left(2e^3\right)\int \frac{60(1-\frac{e^3}{3})-60(1-\frac{e^3}{60})x-60(1-\frac{e^3}{3})\log (2x)+60x\log (2x)}{{(3-2^{20/x}{x}^{20/x})}^2}dx+\left(120e^6\right)\int \frac{-1+\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^3}dx\\ & =2\int (x-3x^2+2x^3)dx+\left(2e^3\right)\int \frac{e^3(-20+x)-60(-1+x)+20(-3+e^3+3x)\log (2x)}{{(3-2^{20/x}{x}^{20/x})}^2}dx+\left(2e^3\right)\int (\frac{20}{-3+2^{20/x}{x}^{20/x}}-\frac{22x}{-3+2^{20/x}{x}^{20/x}}+\frac{3x^2}{-3+2^{20/x}{x}^{20/x}}-\frac{20\log (2x)}{-3+2^{20/x}{x}^{20/x}}+\frac{20x\log (2x)}{-3+2^{20/x}{x}^{20/x}})dx+\left(120e^6\right)\int (-\frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}+\frac{\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^3})dx\\ & =x^2-2x^3+x^4+\left(2e^3\right)\int (\frac{60(1-\frac{e^3}{3})}{{(-3+2^{20/x}{x}^{20/x})}^2}-\frac{60(1-\frac{e^3}{60})x}{{(-3+2^{20/x}{x}^{20/x})}^2}-\frac{60(1-\frac{e^3}{3})\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^2}+\frac{60x\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^2})dx+\left(6e^3\right)\int \frac{x^2}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx-\left(40e^3\right)\int \frac{\log (2x)}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{x\log (2x)}{-3+2^{20/x}{x}^{20/x}}dx-\left(44e^3\right)\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx-\left(120e^6\right)\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx+\left(120e^6\right)\int \frac{\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^3}dx\\ & =x^2-2x^3+x^4+\left(6e^3\right)\int \frac{x^2}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx}{x}dx-\left(40e^3\right)\int \frac{\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx}{x}dx-\left(44e^3\right)\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx+\left(120e^3\right)\int \frac{x\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^2}dx-\left(120e^6\right)\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx-\left(120e^6\right)\int \frac{\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx}{x}dx+\left(40e^3(3-e^3)\right)\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^2}dx-\left(40e^3(3-e^3)\right)\int \frac{\log (2x)}{{(-3+2^{20/x}{x}^{20/x})}^2}dx-\left(2e^3(60-e^3)\right)\int \frac{x}{{(-3+2^{20/x}{x}^{20/x})}^2}dx-(40e^3\log (2x))\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx+(40e^3\log (2x))\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx+(120e^6\log (2x))\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx\\ & =x^2-2x^3+x^4+\left(6e^3\right)\int \frac{x^2}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx+\left(40e^3\right)\int \frac{\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx}{x}dx-\left(40e^3\right)\int \frac{\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx}{x}dx-\left(44e^3\right)\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx-\left(120e^3\right)\int \frac{\int \frac{x}{{(-3+2^{20/x}{x}^{20/x})}^2}dx}{x}dx-\left(120e^6\right)\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx-\left(120e^6\right)\int \frac{\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx}{x}dx+\left(40e^3(3-e^3)\right)\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^2}dx+\left(40e^3(3-e^3)\right)\int \frac{\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^2}dx}{x}dx-\left(2e^3(60-e^3)\right)\int \frac{x}{{(-3+2^{20/x}{x}^{20/x})}^2}dx-(40e^3\log (2x))\int \frac{1}{-3+2^{20/x}{x}^{20/x}}dx+(40e^3\log (2x))\int \frac{x}{-3+2^{20/x}{x}^{20/x}}dx+(120e^3\log (2x))\int \frac{x}{{(-3+2^{20/x}{x}^{20/x})}^2}dx+(120e^6\log (2x))\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^3}dx-(40e^3(3-e^3)\log (2x))\int \frac{1}{{(-3+2^{20/x}{x}^{20/x})}^2}dx\end{array}\end{array}$$

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Mathematica [F]  time = 1.31, size = 0, normalized size = 0.00 $$\begin{array}{c}\int \frac{-54x-6e^{6}x+162x^2-108x^3+e^3(-36x+54x^2)+2^{60/x}{x}^{60/x}(2x-6x^2+4x^3)+2^{20/x}{x}^{20/x}(54x-162x^2+108x^3+e^6(-40+2x)+e^3(-120+144x-36x^2)+(40e^6+e^3(120-120x))\log (2x))+2^{40/x}{x}^{40/x}(-18x+54x^2-36x^3+e^3(40-44x+6x^2)+e^3(-40+40x)\log (2x))}{-27+272^{20/x}{x}^{20/x}-92^{40/x}{x}^{40/x}+2^{60/x}{x}^{60/x}}dx\end{array}$$

Verification is not applicable to the result.

[In]

Integrate[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^(60/x)*x^(60/x)*(2*x - 6*x^2 + 4*x^3
) + 2^(20/x)*x^(20/x)*(54*x - 162*x^2 + 108*x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^
3*(120 - 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^3*(40 - 44*x + 6*x^2) + E^3*(-40 +
40*x)*Log[2*x]))/(-27 + 27*2^(20/x)*x^(20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/x)),x]

[Out]

Integrate[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^(60/x)*x^(60/x)*(2*x - 6*x^2 + 4*x^3
) + 2^(20/x)*x^(20/x)*(54*x - 162*x^2 + 108*x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^
3*(120 - 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^3*(40 - 44*x + 6*x^2) + E^3*(-40 +
40*x)*Log[2*x]))/(-27 + 27*2^(20/x)*x^(20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/x)), x]

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fricas [B]  time = 0.74, size = 122, normalized size = 3.49 $$\begin{array}{c}\frac{9x^4-18x^3+x^2{e}^6+(x^4-2x^3+x^2){\left(2x\right)}^{\frac{40}{x}}-2(3x^4-6x^3+3x^2-(x^3-x^2)e^3){\left(2x\right)}^{\frac{20}{x}}+9x^2-6(x^3-x^2)e^3}{{\left(2x\right)}^{\frac{40}{x}}-6{\left(2x\right)}^{\frac{20}{x}}+9}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^3-6*x^2+2*x)*exp(20*log(2*x)/x)^3+((40*x-40)*exp(3)*log(2*x)+(6*x^2-44*x+40)*exp(3)-36*x^3+54*
x^2-18*x)*exp(20*log(2*x)/x)^2+((40*exp(3)^2+(-120*x+120)*exp(3))*log(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-12
0)*exp(3)+108*x^3-162*x^2+54*x)*exp(20*log(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-108*x^3+162*x^2-54*x)/(ex
p(20*log(2*x)/x)^3-9*exp(20*log(2*x)/x)^2+27*exp(20*log(2*x)/x)-27),x, algorithm="fricas")

[Out]

(9*x^4 - 18*x^3 + x^2*e^6 + (x^4 - 2*x^3 + x^2)*(2*x)^(40/x) - 2*(3*x^4 - 6*x^3 + 3*x^2 - (x^3 - x^2)*e^3)*(2*
x)^(20/x) + 9*x^2 - 6*(x^3 - x^2)*e^3)/((2*x)^(40/x) - 6*(2*x)^(20/x) + 9)

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Exception raised: TypeError}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^3-6*x^2+2*x)*exp(20*log(2*x)/x)^3+((40*x-40)*exp(3)*log(2*x)+(6*x^2-44*x+40)*exp(3)-36*x^3+54*
x^2-18*x)*exp(20*log(2*x)/x)^2+((40*exp(3)^2+(-120*x+120)*exp(3))*log(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-12
0)*exp(3)+108*x^3-162*x^2+54*x)*exp(20*log(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-108*x^3+162*x^2-54*x)/(ex
p(20*log(2*x)/x)^3-9*exp(20*log(2*x)/x)^2+27*exp(20*log(2*x)/x)-27),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 0.54Unable to divide, perhaps due to rounding error%%%{265420800000,[1,10,15,0]%%%}+%%%{-3
98131200000

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maple [B]  time = 0.08, size = 62, normalized size = 1.77

method	result	size
risch	$x^4-2x^3+x^2+\frac{(2{\left(2x\right)}^{\frac{20}{x}}x+{\mathrm{e}}^3-6x-2{\left(2x\right)}^{\frac{20}{x}}+6)x^2{\mathrm{e}}^3}{{({\left(2x\right)}^{\frac{20}{x}}-3)}^2}$	$62$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^3-6*x^2+2*x)*exp(20*ln(2*x)/x)^3+((40*x-40)*exp(3)*ln(2*x)+(6*x^2-44*x+40)*exp(3)-36*x^3+54*x^2-18*x
)*exp(20*ln(2*x)/x)^2+((40*exp(3)^2+(-120*x+120)*exp(3))*ln(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-120)*exp(3)+
108*x^3-162*x^2+54*x)*exp(20*ln(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-108*x^3+162*x^2-54*x)/(exp(20*ln(2*x
)/x)^3-9*exp(20*ln(2*x)/x)^2+27*exp(20*ln(2*x)/x)-27),x,method=_RETURNVERBOSE)

[Out]

x^4-2*x^3+x^2+(2*(2*x)^(20/x)*x+exp(3)-6*x-2*(2*x)^(20/x)+6)*x^2*exp(3)/((2*x)^(20/x)-3)^2

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maxima [B]  time = 0.78, size = 136, normalized size = 3.89 $$\begin{array}{c}\frac{9x^4-6x^3(e^3+3)+x^2(e^6+6e^3+9)+(x^4-2x^3+x^2)e^{(\frac{40\log (2)}{x}+\frac{40\log (x)}{x})}-2(3x^4-x^3(e^3+6)+x^2(e^3+3))e^{(\frac{20\log (2)}{x}+\frac{20\log (x)}{x})}}{e^{(\frac{40\log (2)}{x}+\frac{40\log (x)}{x})}-6e^{(\frac{20\log (2)}{x}+\frac{20\log (x)}{x})}+9}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^3-6*x^2+2*x)*exp(20*log(2*x)/x)^3+((40*x-40)*exp(3)*log(2*x)+(6*x^2-44*x+40)*exp(3)-36*x^3+54*
x^2-18*x)*exp(20*log(2*x)/x)^2+((40*exp(3)^2+(-120*x+120)*exp(3))*log(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-12
0)*exp(3)+108*x^3-162*x^2+54*x)*exp(20*log(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-108*x^3+162*x^2-54*x)/(ex
p(20*log(2*x)/x)^3-9*exp(20*log(2*x)/x)^2+27*exp(20*log(2*x)/x)-27),x, algorithm="maxima")

[Out]

(9*x^4 - 6*x^3*(e^3 + 3) + x^2*(e^6 + 6*e^3 + 9) + (x^4 - 2*x^3 + x^2)*e^(40*log(2)/x + 40*log(x)/x) - 2*(3*x^
4 - x^3*(e^3 + 6) + x^2*(e^3 + 3))*e^(20*log(2)/x + 20*log(x)/x))/(e^(40*log(2)/x + 40*log(x)/x) - 6*e^(20*log
(2)/x + 20*log(x)/x) + 9)

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mupad [B]  time = 1.38, size = 139, normalized size = 3.97 $$\begin{array}{c}{x}^2-2x^3+x^4-\frac{x^2{\mathrm{e}}^6-x^2\ln \left(2x\right){\mathrm{e}}^6}{(\ln \left(2x\right)-1)(2^{40/x}{x}^{40/x}-62^{20/x}{x}^{20/x}+9)}+\frac{2(x^2{\mathrm{e}}^3-x^3{\mathrm{e}}^3-x^2\ln \left(2x\right){\mathrm{e}}^3+x^3\ln \left(2x\right){\mathrm{e}}^3)}{(2^{20/x}{x}^{20/x}-3)(\ln \left(2x\right)-1)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(54*x + exp(3)*(36*x - 54*x^2) + 6*x*exp(6) - exp((40*log(2*x))/x)*(exp(3)*(6*x^2 - 44*x + 40) - 18*x + 5
4*x^2 - 36*x^3 + log(2*x)*exp(3)*(40*x - 40)) - exp((20*log(2*x))/x)*(54*x - exp(3)*(36*x^2 - 144*x + 120) + l
og(2*x)*(40*exp(6) - exp(3)*(120*x - 120)) - 162*x^2 + 108*x^3 + exp(6)*(2*x - 40)) - 162*x^2 + 108*x^3 - exp(
(60*log(2*x))/x)*(2*x - 6*x^2 + 4*x^3))/(27*exp((20*log(2*x))/x) - 9*exp((40*log(2*x))/x) + exp((60*log(2*x))/
x) - 27),x)

[Out]

x^2 - 2*x^3 + x^4 - (x^2*exp(6) - x^2*log(2*x)*exp(6))/((log(2*x) - 1)*(2^(40/x)*x^(40/x) - 6*2^(20/x)*x^(20/x
) + 9)) + (2*(x^2*exp(3) - x^3*exp(3) - x^2*log(2*x)*exp(3) + x^3*log(2*x)*exp(3)))/((2^(20/x)*x^(20/x) - 3)*(
log(2*x) - 1))

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sympy [B]  time = 0.48, size = 85, normalized size = 2.43 $$\begin{array}{c}{x}^4-2x^3+x^2+\frac{-6x^3{e}^3+6x^2{e}^3+x^2{e}^6+(2x^3{e}^3-2x^2{e}^3)e^{\frac{20\log \left(2x\right)}{x}}}{e^{\frac{40\log \left(2x\right)}{x}}-6e^{\frac{20\log \left(2x\right)}{x}}+9}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**3-6*x**2+2*x)*exp(20*ln(2*x)/x)**3+((40*x-40)*exp(3)*ln(2*x)+(6*x**2-44*x+40)*exp(3)-36*x**3+
54*x**2-18*x)*exp(20*ln(2*x)/x)**2+((40*exp(3)**2+(-120*x+120)*exp(3))*ln(2*x)+(2*x-40)*exp(3)**2+(-36*x**2+14
4*x-120)*exp(3)+108*x**3-162*x**2+54*x)*exp(20*ln(2*x)/x)-6*x*exp(3)**2+(54*x**2-36*x)*exp(3)-108*x**3+162*x**
2-54*x)/(exp(20*ln(2*x)/x)**3-9*exp(20*ln(2*x)/x)**2+27*exp(20*ln(2*x)/x)-27),x)

[Out]

x**4 - 2*x**3 + x**2 + (-6*x**3*exp(3) + 6*x**2*exp(3) + x**2*exp(6) + (2*x**3*exp(3) - 2*x**2*exp(3))*exp(20*
log(2*x)/x))/(exp(40*log(2*x)/x) - 6*exp(20*log(2*x)/x) + 9)

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