3.17.28 \(\int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 (-36 x+54 x^2)+2^{60/x} x^{60/x} (2 x-6 x^2+4 x^3)+2^{20/x} x^{20/x} (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 (-120+144 x-36 x^2)+(40 e^6+e^3 (120-120 x)) \log (2 x))+2^{40/x} x^{40/x} (-18 x+54 x^2-36 x^3+e^3 (40-44 x+6 x^2)+e^3 (-40+40 x) \log (2 x))}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx\)

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

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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 {gather*} \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-54-6 e^6\right ) x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx\\ &=\int \frac {-\left (\left (-54-6 e^6\right ) x\right )-162 x^2+108 x^3-e^3 \left (-36 x+54 x^2\right )-2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )-2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )-2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{\left (3-2^{20/x} x^{20/x}\right )^3} \, dx\\ &=\int \left (2 x \left (1-3 x+2 x^2\right )+\frac {120 e^6 (-1+\log (2 x))}{\left (-3+2^{20/x} x^{20/x}\right )^3}+\frac {2 e^3 \left (20-22 x+3 x^2-20 \log (2 x)+20 x \log (2 x)\right )}{-3+2^{20/x} x^{20/x}}+\frac {2 e^3 \left (60 \left (1-\frac {e^3}{3}\right )-60 \left (1-\frac {e^3}{60}\right ) x-60 \left (1-\frac {e^3}{3}\right ) \log (2 x)+60 x \log (2 x)\right )}{\left (3-2^{20/x} x^{20/x}\right )^2}\right ) \, dx\\ &=2 \int x \left (1-3 x+2 x^2\right ) \, dx+\left (2 e^3\right ) \int \frac {20-22 x+3 x^2-20 \log (2 x)+20 x \log (2 x)}{-3+2^{20/x} x^{20/x}} \, dx+\left (2 e^3\right ) \int \frac {60 \left (1-\frac {e^3}{3}\right )-60 \left (1-\frac {e^3}{60}\right ) x-60 \left (1-\frac {e^3}{3}\right ) \log (2 x)+60 x \log (2 x)}{\left (3-2^{20/x} x^{20/x}\right )^2} \, dx+\left (120 e^6\right ) \int \frac {-1+\log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx\\ &=2 \int \left (x-3 x^2+2 x^3\right ) \, dx+\left (2 e^3\right ) \int \frac {e^3 (-20+x)-60 (-1+x)+20 \left (-3+e^3+3 x\right ) \log (2 x)}{\left (3-2^{20/x} x^{20/x}\right )^2} \, dx+\left (2 e^3\right ) \int \left (\frac {20}{-3+2^{20/x} x^{20/x}}-\frac {22 x}{-3+2^{20/x} x^{20/x}}+\frac {3 x^2}{-3+2^{20/x} x^{20/x}}-\frac {20 \log (2 x)}{-3+2^{20/x} x^{20/x}}+\frac {20 x \log (2 x)}{-3+2^{20/x} x^{20/x}}\right ) \, dx+\left (120 e^6\right ) \int \left (-\frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3}+\frac {\log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^3}\right ) \, dx\\ &=x^2-2 x^3+x^4+\left (2 e^3\right ) \int \left (\frac {60 \left (1-\frac {e^3}{3}\right )}{\left (-3+2^{20/x} x^{20/x}\right )^2}-\frac {60 \left (1-\frac {e^3}{60}\right ) x}{\left (-3+2^{20/x} x^{20/x}\right )^2}-\frac {60 \left (1-\frac {e^3}{3}\right ) \log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^2}+\frac {60 x \log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^2}\right ) \, dx+\left (6 e^3\right ) \int \frac {x^2}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx-\left (40 e^3\right ) \int \frac {\log (2 x)}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {x \log (2 x)}{-3+2^{20/x} x^{20/x}} \, dx-\left (44 e^3\right ) \int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx-\left (120 e^6\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx+\left (120 e^6\right ) \int \frac {\log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx\\ &=x^2-2 x^3+x^4+\left (6 e^3\right ) \int \frac {x^2}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {\int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx}{x} \, dx-\left (40 e^3\right ) \int \frac {\int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx}{x} \, dx-\left (44 e^3\right ) \int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx+\left (120 e^3\right ) \int \frac {x \log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx-\left (120 e^6\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx-\left (120 e^6\right ) \int \frac {\int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx}{x} \, dx+\left (40 e^3 \left (3-e^3\right )\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx-\left (40 e^3 \left (3-e^3\right )\right ) \int \frac {\log (2 x)}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx-\left (2 e^3 \left (60-e^3\right )\right ) \int \frac {x}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx-\left (40 e^3 \log (2 x)\right ) \int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3 \log (2 x)\right ) \int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx+\left (120 e^6 \log (2 x)\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx\\ &=x^2-2 x^3+x^4+\left (6 e^3\right ) \int \frac {x^2}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3\right ) \int \frac {\int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx}{x} \, dx-\left (40 e^3\right ) \int \frac {\int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx}{x} \, dx-\left (44 e^3\right ) \int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx-\left (120 e^3\right ) \int \frac {\int \frac {x}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx}{x} \, dx-\left (120 e^6\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx-\left (120 e^6\right ) \int \frac {\int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx}{x} \, dx+\left (40 e^3 \left (3-e^3\right )\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx+\left (40 e^3 \left (3-e^3\right )\right ) \int \frac {\int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx}{x} \, dx-\left (2 e^3 \left (60-e^3\right )\right ) \int \frac {x}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx-\left (40 e^3 \log (2 x)\right ) \int \frac {1}{-3+2^{20/x} x^{20/x}} \, dx+\left (40 e^3 \log (2 x)\right ) \int \frac {x}{-3+2^{20/x} x^{20/x}} \, dx+\left (120 e^3 \log (2 x)\right ) \int \frac {x}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx+\left (120 e^6 \log (2 x)\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^3} \, dx-\left (40 e^3 \left (3-e^3\right ) \log (2 x)\right ) \int \frac {1}{\left (-3+2^{20/x} x^{20/x}\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 1.31, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx \end {gather*}

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 {gather*} \frac {9 \, x^{4} - 18 \, x^{3} + x^{2} e^{6} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \left (2 \, x\right )^{\frac {40}{x}} - 2 \, {\left (3 \, x^{4} - 6 \, x^{3} + 3 \, x^{2} - {\left (x^{3} - x^{2}\right )} e^{3}\right )} \left (2 \, x\right )^{\frac {20}{x}} + 9 \, x^{2} - 6 \, {\left (x^{3} - x^{2}\right )} e^{3}}{\left (2 \, x\right )^{\frac {40}{x}} - 6 \, \left (2 \, x\right )^{\frac {20}{x}} + 9} \end {gather*}

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 {gather*} \text {Exception raised: TypeError} \end {gather*}

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

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 {gather*} \frac {9 \, x^{4} - 6 \, x^{3} {\left (e^{3} + 3\right )} + x^{2} {\left (e^{6} + 6 \, e^{3} + 9\right )} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (\frac {40 \, \log \relax (2)}{x} + \frac {40 \, \log \relax (x)}{x}\right )} - 2 \, {\left (3 \, x^{4} - x^{3} {\left (e^{3} + 6\right )} + x^{2} {\left (e^{3} + 3\right )}\right )} e^{\left (\frac {20 \, \log \relax (2)}{x} + \frac {20 \, \log \relax (x)}{x}\right )}}{e^{\left (\frac {40 \, \log \relax (2)}{x} + \frac {40 \, \log \relax (x)}{x}\right )} - 6 \, e^{\left (\frac {20 \, \log \relax (2)}{x} + \frac {20 \, \log \relax (x)}{x}\right )} + 9} \end {gather*}

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 {gather*} x^2-2\,x^3+x^4-\frac {x^2\,{\mathrm {e}}^6-x^2\,\ln \left (2\,x\right )\,{\mathrm {e}}^6}{\left (\ln \left (2\,x\right )-1\right )\,\left (2^{40/x}\,x^{40/x}-6\,2^{20/x}\,x^{20/x}+9\right )}+\frac {2\,\left (x^2\,{\mathrm {e}}^3-x^3\,{\mathrm {e}}^3-x^2\,\ln \left (2\,x\right )\,{\mathrm {e}}^3+x^3\,\ln \left (2\,x\right )\,{\mathrm {e}}^3\right )}{\left (2^{20/x}\,x^{20/x}-3\right )\,\left (\ln \left (2\,x\right )-1\right )} \end {gather*}

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 {gather*} x^{4} - 2 x^{3} + x^{2} + \frac {- 6 x^{3} e^{3} + 6 x^{2} e^{3} + x^{2} e^{6} + \left (2 x^{3} e^{3} - 2 x^{2} e^{3}\right ) e^{\frac {20 \log {\left (2 x \right )}}{x}}}{e^{\frac {40 \log {\left (2 x \right )}}{x}} - 6 e^{\frac {20 \log {\left (2 x \right )}}{x}} + 9} \end {gather*}

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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