∫ 2x+x2+x3+e8x4 (−8+4x2) log3( x____ 2+x+x2 )+e8x4 (−64x4−32x5−32x6) log4( x____ 2+x+x2 ) ____________________________________________________________________________________________________________

3.78.15 \(\int \frac {2 x+x^2+x^3+e^{8 x^4} (-8+4 x^2) \log ^3(\frac {x}{2+x+x^2})+e^{8 x^4} (-64 x^4-32 x^5-32 x^6) \log ^4(\frac {x}{2+x+x^2})}{2 x+x^2+x^3} \, dx\)

Optimal. Leaf size=24 \[ x-e^{8 x^4} \log ^4\left (\frac {x}{2+x+x^2}\right ) \]

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Rubi [F] time = 2.36, 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 {2 x+x^2+x^3+e^{8 x^4} \left (-8+4 x^2\right ) \log ^3\left (\frac {x}{2+x+x^2}\right )+e^{8 x^4} \left (-64 x^4-32 x^5-32 x^6\right ) \log ^4\left (\frac {x}{2+x+x^2}\right )}{2 x+x^2+x^3} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(2*x + x^2 + x^3 + E^(8*x^4)*(-8 + 4*x^2)*Log[x/(2 + x + x^2)]^3 + E^(8*x^4)*(-64*x^4 - 32*x^5 - 32*x^6)*L

og[x/(2 + x + x^2)]^4)/(2*x + x^2 + x^3),x]

[Out]

x + ((8*I)*Defer[Int][(E^(8*x^4)*Log[x/(2 + x + x^2)]^3)/(-1 + I*Sqrt[7] - 2*x), x])/Sqrt[7] - 4*Defer[Int][(E

^(8*x^4)*Log[x/(2 + x + x^2)]^3)/x, x] + (8*(7 + I*Sqrt[7])*Defer[Int][(E^(8*x^4)*Log[x/(2 + x + x^2)]^3)/(1 -

I*Sqrt[7] + 2*x), x])/7 + ((8*I)*Defer[Int][(E^(8*x^4)*Log[x/(2 + x + x^2)]^3)/(1 + I*Sqrt[7] + 2*x), x])/Sqr

t[7] + (8*(7 - I*Sqrt[7])*Defer[Int][(E^(8*x^4)*Log[x/(2 + x + x^2)]^3)/(1 + I*Sqrt[7] + 2*x), x])/7 - 32*Defe

r[Int][E^(8*x^4)*x^3*Log[x/(2 + x + x^2)]^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x+x^2+x^3+e^{8 x^4} \left (-8+4 x^2\right ) \log ^3\left (\frac {x}{2+x+x^2}\right )+e^{8 x^4} \left (-64 x^4-32 x^5-32 x^6\right ) \log ^4\left (\frac {x}{2+x+x^2}\right )}{x \left (2+x+x^2\right )} \, dx\\ &=\int \left (1+\frac {4 e^{8 x^4} \left (-2+x^2\right ) \log ^3\left (\frac {x}{2+x+x^2}\right )}{x \left (2+x+x^2\right )}-32 e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right )\right ) \, dx\\ &=x+4 \int \frac {e^{8 x^4} \left (-2+x^2\right ) \log ^3\left (\frac {x}{2+x+x^2}\right )}{x \left (2+x+x^2\right )} \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x+4 \int \left (-\frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x}+\frac {e^{8 x^4} (1+2 x) \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2}\right ) \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x-4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x} \, dx+4 \int \frac {e^{8 x^4} (1+2 x) \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2} \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x-4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x} \, dx+4 \int \left (\frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2}+\frac {2 e^{8 x^4} x \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2}\right ) \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x-4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x} \, dx+4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2} \, dx+8 \int \frac {e^{8 x^4} x \log ^3\left (\frac {x}{2+x+x^2}\right )}{2+x+x^2} \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x-4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x} \, dx+4 \int \left (\frac {2 i e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{\sqrt {7} \left (-1+i \sqrt {7}-2 x\right )}+\frac {2 i e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{\sqrt {7} \left (1+i \sqrt {7}+2 x\right )}\right ) \, dx+8 \int \left (\frac {\left (1+\frac {i}{\sqrt {7}}\right ) e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{1-i \sqrt {7}+2 x}+\frac {\left (1-\frac {i}{\sqrt {7}}\right ) e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{1+i \sqrt {7}+2 x}\right ) \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx\\ &=x-4 \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{x} \, dx-32 \int e^{8 x^4} x^3 \log ^4\left (\frac {x}{2+x+x^2}\right ) \, dx+\frac {(8 i) \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{-1+i \sqrt {7}-2 x} \, dx}{\sqrt {7}}+\frac {(8 i) \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{1+i \sqrt {7}+2 x} \, dx}{\sqrt {7}}+\frac {1}{7} \left (8 \left (7-i \sqrt {7}\right )\right ) \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{1+i \sqrt {7}+2 x} \, dx+\frac {1}{7} \left (8 \left (7+i \sqrt {7}\right )\right ) \int \frac {e^{8 x^4} \log ^3\left (\frac {x}{2+x+x^2}\right )}{1-i \sqrt {7}+2 x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F] time = 0.76, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 x+x^2+x^3+e^{8 x^4} \left (-8+4 x^2\right ) \log ^3\left (\frac {x}{2+x+x^2}\right )+e^{8 x^4} \left (-64 x^4-32 x^5-32 x^6\right ) \log ^4\left (\frac {x}{2+x+x^2}\right )}{2 x+x^2+x^3} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Integrate[(2*x + x^2 + x^3 + E^(8*x^4)*(-8 + 4*x^2)*Log[x/(2 + x + x^2)]^3 + E^(8*x^4)*(-64*x^4 - 32*x^5 - 32*

x^6)*Log[x/(2 + x + x^2)]^4)/(2*x + x^2 + x^3),x]

[Out]

Integrate[(2*x + x^2 + x^3 + E^(8*x^4)*(-8 + 4*x^2)*Log[x/(2 + x + x^2)]^3 + E^(8*x^4)*(-64*x^4 - 32*x^5 - 32*

x^6)*Log[x/(2 + x + x^2)]^4)/(2*x + x^2 + x^3), x]

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fricas [A] time = 0.61, size = 23, normalized size = 0.96 \begin {gather*} -e^{\left (8 \, x^{4}\right )} \log \left (\frac {x}{x^{2} + x + 2}\right )^{4} + x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6-32*x^5-64*x^4)*exp(2*x^4)^4*log(x/(x^2+x+2))^4+(4*x^2-8)*exp(2*x^4)^4*log(x/(x^2+x+2))^3+x

^3+x^2+2*x)/(x^3+x^2+2*x),x, algorithm="fricas")

[Out]

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

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giac [A] time = 0.55, size = 23, normalized size = 0.96 \begin {gather*} -e^{\left (8 \, x^{4}\right )} \log \left (\frac {x}{x^{2} + x + 2}\right )^{4} + x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6-32*x^5-64*x^4)*exp(2*x^4)^4*log(x/(x^2+x+2))^4+(4*x^2-8)*exp(2*x^4)^4*log(x/(x^2+x+2))^3+x

^3+x^2+2*x)/(x^3+x^2+2*x),x, algorithm="giac")

[Out]

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

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maple [C] time = 0.47, size = 4181, normalized size = 174.21


method	result	size

risch	\(\text {Expression too large to display}\)	\(4181\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-32*x^6-32*x^5-64*x^4)*exp(2*x^4)^4*ln(x/(x^2+x+2))^4+(4*x^2-8)*exp(2*x^4)^4*ln(x/(x^2+x+2))^3+x^3+x^2+2

*x)/(x^3+x^2+2*x),x,method=_RETURNVERBOSE)

[Out]

x-3/8*Pi^4*csgn(I*x/(x^2+x+2))^10*csgn(I*x)^2*exp(8*x^4)+1/4*Pi^4*csgn(I*x/(x^2+x+2))^9*csgn(I*x)^3*exp(8*x^4)

-1/16*Pi^4*csgn(I*x/(x^2+x+2))^8*csgn(I*x)^4*exp(8*x^4)+3/2*Pi^2*csgn(I*x/(x^2+x+2))^6*exp(8*x^4)*ln(x)^2-1/16

*Pi^4*csgn(I/(x^2+x+2))^4*csgn(I*x/(x^2+x+2))^8*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^9*

exp(8*x^4)-3/8*Pi^4*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^10*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))*csgn(I*x/

(x^2+x+2))^11*exp(8*x^4)+1/4*Pi^4*csgn(I*x/(x^2+x+2))^11*csgn(I*x)*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))^4*csg

n(I*x/(x^2+x+2))^7*csgn(I*x)*exp(8*x^4)-3/8*Pi^4*csgn(I/(x^2+x+2))^4*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^2*exp(8*x

^4)-3*Pi^2*csgn(I*x/(x^2+x+2))^5*csgn(I*x)*exp(8*x^4)*ln(x)^2-Pi^4*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^8*csg

n(I*x)^3*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^7*csgn(I*x)^4*exp(8*x^4)-Pi^4*csgn(I/(x^2+x

+2))^3*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^3*exp(8*x^4)-exp(8*x^4)*ln(x)^4-exp(8*x^4)*ln(x^2+x+2)^4+3/2*I*Pi^3*csg

n(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^4*csgn(I*x)^3*exp(8*x^4)*ln(x)-9/2*I*Pi^3*csgn(I/(x^2+x+2))*csgn(I*x/(x^2

+x+2))^7*csgn(I*x)*exp(8*x^4)*ln(x)+(-6*exp(8*x^4)*ln(x)^2-6*I*Pi*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^2*exp(

8*x^4)*ln(x)+6*I*Pi*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))*csgn(I*x)*exp(8*x^4)*ln(x)+6*I*Pi*csgn(I*x/(x^2+x+2)

)^3*exp(8*x^4)*ln(x)-6*I*Pi*csgn(I*x/(x^2+x+2))^2*csgn(I*x)*exp(8*x^4)*ln(x)+3/2*Pi^2*csgn(I/(x^2+x+2))^2*csgn

(I*x/(x^2+x+2))^4*exp(8*x^4)-3*Pi^2*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^3*csgn(I*x)*exp(8*x^4)+3/2*Pi^2*cs

gn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^2*csgn(I*x)^2*exp(8*x^4)-3*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^5*

exp(8*x^4)+6*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^4*csgn(I*x)*exp(8*x^4)-3*Pi^2*csgn(I/(x^2+x+2))*csgn(I

*x/(x^2+x+2))^3*csgn(I*x)^2*exp(8*x^4)+3/2*Pi^2*csgn(I*x/(x^2+x+2))^6*exp(8*x^4)-3*Pi^2*csgn(I*x/(x^2+x+2))^5*

csgn(I*x)*exp(8*x^4)+3/2*Pi^2*csgn(I*x/(x^2+x+2))^4*csgn(I*x)^2*exp(8*x^4))*ln(x^2+x+2)^2+(2*I*Pi*csgn(I/(x^2+

x+2))*csgn(I*x/(x^2+x+2))^2*exp(8*x^4)-2*I*Pi*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))*csgn(I*x)*exp(8*x^4)-2*I*P

i*csgn(I*x/(x^2+x+2))^3*exp(8*x^4)+2*I*Pi*csgn(I*x/(x^2+x+2))^2*csgn(I*x)*exp(8*x^4)+4*exp(8*x^4)*ln(x))*ln(x^

2+x+2)^3-Pi^4*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^10*csgn(I*x)*exp(8*x^4)+3/2*Pi^4*csgn(I/(x^2+x+2))*csgn(I*

x/(x^2+x+2))^9*csgn(I*x)^2*exp(8*x^4)+(-3*exp(8*x^4)*Pi^2*csgn(I*x/(x^2+x+2))^6*ln(x)+1/2*I*exp(8*x^4)*Pi^3*cs

gn(I*x/(x^2+x+2))^9-3/2*I*exp(8*x^4)*Pi^3*csgn(I*x/(x^2+x+2))^8*csgn(I*x)+4*exp(8*x^4)*ln(x)^3+6*exp(8*x^4)*Pi

^2*csgn(I*x/(x^2+x+2))^5*csgn(I*x)*ln(x)-3*exp(8*x^4)*Pi^2*csgn(I*x/(x^2+x+2))^4*csgn(I*x)^2*ln(x)-1/2*I*exp(8

*x^4)*Pi^3*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^3-6*I*exp(8*x^4)*ln(x)^2*Pi*csgn(I*x/(x^2+x+2))^3-6*I*exp(8*x^4)*ln

(x)^2*Pi*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))*csgn(I*x)-3/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))*csgn(I*x/(x^2

+x+2))^8+6*exp(8*x^4)*Pi^2*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^3*csgn(I*x)*ln(x)+1/2*I*exp(8*x^4)*Pi^3*csg

n(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^3*csgn(I*x)^3-3/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2

))^4*csgn(I*x)^3+6*I*exp(8*x^4)*ln(x)^2*Pi*csgn(I*x/(x^2+x+2))^2*csgn(I*x)+6*I*exp(8*x^4)*ln(x)^2*Pi*csgn(I/(x

^2+x+2))*csgn(I*x/(x^2+x+2))^2+9/2*I*exp(8*x^4)*Pi^3*csgn(I*x/(x^2+x+2))^7*csgn(I*x)*csgn(I/(x^2+x+2))-12*exp(

8*x^4)*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^4*csgn(I*x)*ln(x)-3*exp(8*x^4)*Pi^2*csgn(I/(x^2+x+2))^2*csgn

(I*x/(x^2+x+2))^2*csgn(I*x)^2*ln(x)+6*exp(8*x^4)*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^3*csgn(I*x)^2*ln(x

)-9/2*I*exp(8*x^4)*Pi^3*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^2*csgn(I/(x^2+x+2))+3/2*I*exp(8*x^4)*Pi^3*csgn(I*x/(x^

2+x+2))^5*csgn(I*x)^3*csgn(I/(x^2+x+2))+3/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^5*csgn(I

*x)-9/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^6*csgn(I*x)+9/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^

2+x+2))^2*csgn(I*x/(x^2+x+2))^5*csgn(I*x)^2-3/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^4*cs

gn(I*x)^2+3/2*I*exp(8*x^4)*Pi^3*csgn(I*x/(x^2+x+2))^7*csgn(I*x)^2-1/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^3*cs

gn(I*x/(x^2+x+2))^6+3/2*I*exp(8*x^4)*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^7-3*exp(8*x^4)*Pi^2*csgn(I/(

x^2+x+2))^2*csgn(I*x/(x^2+x+2))^4*ln(x)+6*exp(8*x^4)*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^5*ln(x))*ln(x^

2+x+2)+3/2*Pi^4*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^7*csgn(I*x)^3*exp(8*x^4)-3/8*Pi^4*csgn(I/(x^2+x+2))^2*

csgn(I*x/(x^2+x+2))^6*csgn(I*x)^4*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))^4*csgn(I*x/(x^2+x+2))^5*csgn(I*x)^3*ex

p(8*x^4)-1/16*Pi^4*csgn(I/(x^2+x+2))^4*csgn(I*x/(x^2+x+2))^4*csgn(I*x)^4*exp(8*x^4)-Pi^4*csgn(I/(x^2+x+2))^3*c

sgn(I*x/(x^2+x+2))^8*csgn(I*x)*exp(8*x^4)+1/4*Pi^4*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^5*csgn(I*x)^4*exp(8

*x^4)-1/16*Pi^4*csgn(I*x/(x^2+x+2))^12*exp(8*x^4)-3*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^5*exp(8*x^4)*ln

(x)^2+9/2*I*Pi^3*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^2*exp(8*x^4)*ln(x)-3/2*I*Pi^3*csgn(I/(x^2+x

+2))*csgn(I*x/(x^2+x+2))^5*csgn(I*x)^3*exp(8*x^4)*ln(x)+3/2*I*Pi^3*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^4*c

sgn(I*x)^2*exp(8*x^4)*ln(x)-1/2*I*Pi^3*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^3*csgn(I*x)^3*exp(8*x^4)*ln(x)+

3/2*Pi^4*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^7*csgn(I*x)^2*exp(8*x^4)-3/2*I*Pi^3*csgn(I/(x^2+x+2))^3*csgn(

I*x/(x^2+x+2))^5*csgn(I*x)*exp(8*x^4)*ln(x)-3*Pi^2*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^3*csgn(I*x)*exp(8*x

^4)*ln(x)^2+3/2*Pi^2*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^2*csgn(I*x)^2*exp(8*x^4)*ln(x)^2+6*Pi^2*csgn(I/(x

^2+x+2))*csgn(I*x/(x^2+x+2))^4*csgn(I*x)*exp(8*x^4)*ln(x)^2-3*Pi^2*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^3*csg

n(I*x)^2*exp(8*x^4)*ln(x)^2-2*I*Pi*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^2*exp(8*x^4)*ln(x)^3-2*I*Pi*csgn(I*x/

(x^2+x+2))^2*csgn(I*x)*exp(8*x^4)*ln(x)^3+1/2*I*Pi^3*csgn(I/(x^2+x+2))^3*csgn(I*x/(x^2+x+2))^6*exp(8*x^4)*ln(x

)-1/2*I*Pi^3*csgn(I*x/(x^2+x+2))^9*exp(8*x^4)*ln(x)+2*I*Pi*csgn(I*x/(x^2+x+2))^3*exp(8*x^4)*ln(x)^3+3/2*Pi^4*c

sgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^9*csgn(I*x)*exp(8*x^4)-9/4*Pi^4*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))

^8*csgn(I*x)^2*exp(8*x^4)+3/2*Pi^2*csgn(I*x/(x^2+x+2))^4*csgn(I*x)^2*exp(8*x^4)*ln(x)^2+2*I*Pi*csgn(I/(x^2+x+2

))*csgn(I*x/(x^2+x+2))*csgn(I*x)*exp(8*x^4)*ln(x)^3+9/2*I*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^6*csgn(

I*x)*exp(8*x^4)*ln(x)-9/2*I*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^5*csgn(I*x)^2*exp(8*x^4)*ln(x)+3/2*Pi

^2*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x+2))^4*exp(8*x^4)*ln(x)^2-3/2*I*Pi^3*csgn(I/(x^2+x+2))^2*csgn(I*x/(x^2+x

+2))^7*exp(8*x^4)*ln(x)+3/2*I*Pi^3*csgn(I/(x^2+x+2))*csgn(I*x/(x^2+x+2))^8*exp(8*x^4)*ln(x)+3/2*I*Pi^3*csgn(I*

x/(x^2+x+2))^8*csgn(I*x)*exp(8*x^4)*ln(x)-3/2*I*Pi^3*csgn(I*x/(x^2+x+2))^7*csgn(I*x)^2*exp(8*x^4)*ln(x)+1/2*I*

Pi^3*csgn(I*x/(x^2+x+2))^6*csgn(I*x)^3*exp(8*x^4)*ln(x)

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maxima [B] time = 0.51, size = 90, normalized size = 3.75 \begin {gather*} -e^{\left (8 \, x^{4}\right )} \log \left (x^{2} + x + 2\right )^{4} + 4 \, e^{\left (8 \, x^{4}\right )} \log \left (x^{2} + x + 2\right )^{3} \log \relax (x) - 6 \, e^{\left (8 \, x^{4}\right )} \log \left (x^{2} + x + 2\right )^{2} \log \relax (x)^{2} + 4 \, e^{\left (8 \, x^{4}\right )} \log \left (x^{2} + x + 2\right ) \log \relax (x)^{3} - e^{\left (8 \, x^{4}\right )} \log \relax (x)^{4} + x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6-32*x^5-64*x^4)*exp(2*x^4)^4*log(x/(x^2+x+2))^4+(4*x^2-8)*exp(2*x^4)^4*log(x/(x^2+x+2))^3+x

^3+x^2+2*x)/(x^3+x^2+2*x),x, algorithm="maxima")

[Out]

-e^(8*x^4)*log(x^2 + x + 2)^4 + 4*e^(8*x^4)*log(x^2 + x + 2)^3*log(x) - 6*e^(8*x^4)*log(x^2 + x + 2)^2*log(x)^

2 + 4*e^(8*x^4)*log(x^2 + x + 2)*log(x)^3 - e^(8*x^4)*log(x)^4 + x

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mupad [B] time = 5.34, size = 23, normalized size = 0.96 \begin {gather*} x-{\ln \left (\frac {x}{x^2+x+2}\right )}^4\,{\mathrm {e}}^{8\,x^4} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((2*x + x^2 + x^3 + log(x/(x + x^2 + 2))^3*exp(8*x^4)*(4*x^2 - 8) - log(x/(x + x^2 + 2))^4*exp(8*x^4)*(64*x

^4 + 32*x^5 + 32*x^6))/(2*x + x^2 + x^3),x)

[Out]

x - log(x/(x + x^2 + 2))^4*exp(8*x^4)

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sympy [A] time = 57.54, size = 19, normalized size = 0.79 \begin {gather*} x - e^{8 x^{4}} \log {\left (\frac {x}{x^{2} + x + 2} \right )}^{4} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x**6-32*x**5-64*x**4)*exp(2*x**4)**4*ln(x/(x**2+x+2))**4+(4*x**2-8)*exp(2*x**4)**4*ln(x/(x**2+

x+2))**3+x**3+x**2+2*x)/(x**3+x**2+2*x),x)

[Out]

x - exp(8*x**4)*log(x/(x**2 + x + 2))**4

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