3.27.8 \(\int (1+2 e^{2 x}+(-24 e^x x+8 e^{2 x} x^2) \log (x^2)+(e^x (-12 x-6 x^2)+e^{2 x} (6 x^2+4 x^3)) \log ^2(x^2)+(72 x^3-48 e^x x^4+8 e^{2 x} x^5) \log ^3(x^2)+(36 x^3+e^x (-30 x^4-6 x^5)+e^{2 x} (6 x^5+2 x^6)) \log ^4(x^2)) \, dx\)

Optimal. Leaf size=29 \[ 4+x+\left (-e^x+x^2 \left (3-e^x x\right ) \log ^2\left (x^2\right )\right )^2 \]

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Rubi [F]  time = 2.43, 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 \left (1+2 e^{2 x}+\left (-24 e^x x+8 e^{2 x} x^2\right ) \log \left (x^2\right )+\left (e^x \left (-12 x-6 x^2\right )+e^{2 x} \left (6 x^2+4 x^3\right )\right ) \log ^2\left (x^2\right )+\left (72 x^3-48 e^x x^4+8 e^{2 x} x^5\right ) \log ^3\left (x^2\right )+\left (36 x^3+e^x \left (-30 x^4-6 x^5\right )+e^{2 x} \left (6 x^5+2 x^6\right )\right ) \log ^4\left (x^2\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1 + 2*E^(2*x) + (-24*E^x*x + 8*E^(2*x)*x^2)*Log[x^2] + (E^x*(-12*x - 6*x^2) + E^(2*x)*(6*x^2 + 4*x^3))*Log
[x^2]^2 + (72*x^3 - 48*E^x*x^4 + 8*E^(2*x)*x^5)*Log[x^2]^3 + (36*x^3 + E^x*(-30*x^4 - 6*x^5) + E^(2*x)*(6*x^5
+ 2*x^6))*Log[x^2]^4,x]

[Out]

48*E^x + 7*E^(2*x) + x - 4*E^(2*x)*x - 48*ExpIntegralEi[x] - 4*ExpIntegralEi[2*x] + 24*E^x*Log[x^2] + 2*E^(2*x
)*Log[x^2] - 24*E^x*x*Log[x^2] - 4*E^(2*x)*x*Log[x^2] + 4*E^(2*x)*x^2*Log[x^2] + 9*x^4*Log[x^2]^4 - 12*Defer[I
nt][E^x*x*Log[x^2]^2, x] - 6*Defer[Int][E^x*x^2*Log[x^2]^2, x] + 6*Defer[Int][E^(2*x)*x^2*Log[x^2]^2, x] + 4*D
efer[Int][E^(2*x)*x^3*Log[x^2]^2, x] - 48*Defer[Int][E^x*x^4*Log[x^2]^3, x] + 8*Defer[Int][E^(2*x)*x^5*Log[x^2
]^3, x] - 30*Defer[Int][E^x*x^4*Log[x^2]^4, x] - 6*Defer[Int][E^x*x^5*Log[x^2]^4, x] + 6*Defer[Int][E^(2*x)*x^
5*Log[x^2]^4, x] + 2*Defer[Int][E^(2*x)*x^6*Log[x^2]^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+2 \int e^{2 x} \, dx+\int \left (-24 e^x x+8 e^{2 x} x^2\right ) \log \left (x^2\right ) \, dx+\int \left (e^x \left (-12 x-6 x^2\right )+e^{2 x} \left (6 x^2+4 x^3\right )\right ) \log ^2\left (x^2\right ) \, dx+\int \left (72 x^3-48 e^x x^4+8 e^{2 x} x^5\right ) \log ^3\left (x^2\right ) \, dx+\int \left (36 x^3+e^x \left (-30 x^4-6 x^5\right )+e^{2 x} \left (6 x^5+2 x^6\right )\right ) \log ^4\left (x^2\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )-\int \frac {4 e^x \left (-12 (-1+x)+e^x \left (1-2 x+2 x^2\right )\right )}{x} \, dx+\int 2 e^x x \left (-6-3 x+3 e^x x+2 e^x x^2\right ) \log ^2\left (x^2\right ) \, dx+\int 8 x^3 \left (3-e^x x\right )^2 \log ^3\left (x^2\right ) \, dx+\int 2 x^3 \left (18+e^{2 x} x^2 (3+x)-3 e^x x (5+x)\right ) \log ^4\left (x^2\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+2 \int e^x x \left (-6-3 x+3 e^x x+2 e^x x^2\right ) \log ^2\left (x^2\right ) \, dx+2 \int x^3 \left (18+e^{2 x} x^2 (3+x)-3 e^x x (5+x)\right ) \log ^4\left (x^2\right ) \, dx-4 \int \frac {e^x \left (-12 (-1+x)+e^x \left (1-2 x+2 x^2\right )\right )}{x} \, dx+8 \int x^3 \left (3-e^x x\right )^2 \log ^3\left (x^2\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+2 \int \left (-3 e^x x (2+x) \log ^2\left (x^2\right )+e^{2 x} x^2 (3+2 x) \log ^2\left (x^2\right )\right ) \, dx+2 \int \left (18 x^3 \log ^4\left (x^2\right )+e^{2 x} x^5 (3+x) \log ^4\left (x^2\right )-3 e^x x^4 (5+x) \log ^4\left (x^2\right )\right ) \, dx-4 \int \left (-\frac {12 e^x (-1+x)}{x}+\frac {e^{2 x} \left (1-2 x+2 x^2\right )}{x}\right ) \, dx+8 \int \left (9 x^3 \log ^3\left (x^2\right )-6 e^x x^4 \log ^3\left (x^2\right )+e^{2 x} x^5 \log ^3\left (x^2\right )\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+2 \int e^{2 x} x^2 (3+2 x) \log ^2\left (x^2\right ) \, dx+2 \int e^{2 x} x^5 (3+x) \log ^4\left (x^2\right ) \, dx-4 \int \frac {e^{2 x} \left (1-2 x+2 x^2\right )}{x} \, dx-6 \int e^x x (2+x) \log ^2\left (x^2\right ) \, dx-6 \int e^x x^4 (5+x) \log ^4\left (x^2\right ) \, dx+8 \int e^{2 x} x^5 \log ^3\left (x^2\right ) \, dx+36 \int x^3 \log ^4\left (x^2\right ) \, dx+48 \int \frac {e^x (-1+x)}{x} \, dx-48 \int e^x x^4 \log ^3\left (x^2\right ) \, dx+72 \int x^3 \log ^3\left (x^2\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+18 x^4 \log ^3\left (x^2\right )+9 x^4 \log ^4\left (x^2\right )+2 \int \left (3 e^{2 x} x^2 \log ^2\left (x^2\right )+2 e^{2 x} x^3 \log ^2\left (x^2\right )\right ) \, dx+2 \int \left (3 e^{2 x} x^5 \log ^4\left (x^2\right )+e^{2 x} x^6 \log ^4\left (x^2\right )\right ) \, dx-4 \int \left (-2 e^{2 x}+\frac {e^{2 x}}{x}+2 e^{2 x} x\right ) \, dx-6 \int \left (2 e^x x \log ^2\left (x^2\right )+e^x x^2 \log ^2\left (x^2\right )\right ) \, dx-6 \int \left (5 e^x x^4 \log ^4\left (x^2\right )+e^x x^5 \log ^4\left (x^2\right )\right ) \, dx+8 \int e^{2 x} x^5 \log ^3\left (x^2\right ) \, dx+48 \int \left (e^x-\frac {e^x}{x}\right ) \, dx-48 \int e^x x^4 \log ^3\left (x^2\right ) \, dx-72 \int x^3 \log ^3\left (x^2\right ) \, dx-108 \int x^3 \log ^2\left (x^2\right ) \, dx\\ &=e^{2 x}+x+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )-27 x^4 \log ^2\left (x^2\right )+9 x^4 \log ^4\left (x^2\right )+2 \int e^{2 x} x^6 \log ^4\left (x^2\right ) \, dx-4 \int \frac {e^{2 x}}{x} \, dx+4 \int e^{2 x} x^3 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^2 \log ^2\left (x^2\right ) \, dx+6 \int e^{2 x} x^2 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^5 \log ^4\left (x^2\right ) \, dx+6 \int e^{2 x} x^5 \log ^4\left (x^2\right ) \, dx+8 \int e^{2 x} \, dx-8 \int e^{2 x} x \, dx+8 \int e^{2 x} x^5 \log ^3\left (x^2\right ) \, dx-12 \int e^x x \log ^2\left (x^2\right ) \, dx-30 \int e^x x^4 \log ^4\left (x^2\right ) \, dx+48 \int e^x \, dx-48 \int \frac {e^x}{x} \, dx-48 \int e^x x^4 \log ^3\left (x^2\right ) \, dx+108 \int x^3 \log \left (x^2\right ) \, dx+108 \int x^3 \log ^2\left (x^2\right ) \, dx\\ &=48 e^x+5 e^{2 x}+x-4 e^{2 x} x-\frac {27 x^4}{2}-48 \text {Ei}(x)-4 \text {Ei}(2 x)+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+27 x^4 \log \left (x^2\right )+9 x^4 \log ^4\left (x^2\right )+2 \int e^{2 x} x^6 \log ^4\left (x^2\right ) \, dx+4 \int e^{2 x} \, dx+4 \int e^{2 x} x^3 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^2 \log ^2\left (x^2\right ) \, dx+6 \int e^{2 x} x^2 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^5 \log ^4\left (x^2\right ) \, dx+6 \int e^{2 x} x^5 \log ^4\left (x^2\right ) \, dx+8 \int e^{2 x} x^5 \log ^3\left (x^2\right ) \, dx-12 \int e^x x \log ^2\left (x^2\right ) \, dx-30 \int e^x x^4 \log ^4\left (x^2\right ) \, dx-48 \int e^x x^4 \log ^3\left (x^2\right ) \, dx-108 \int x^3 \log \left (x^2\right ) \, dx\\ &=48 e^x+7 e^{2 x}+x-4 e^{2 x} x-48 \text {Ei}(x)-4 \text {Ei}(2 x)+24 e^x \log \left (x^2\right )+2 e^{2 x} \log \left (x^2\right )-24 e^x x \log \left (x^2\right )-4 e^{2 x} x \log \left (x^2\right )+4 e^{2 x} x^2 \log \left (x^2\right )+9 x^4 \log ^4\left (x^2\right )+2 \int e^{2 x} x^6 \log ^4\left (x^2\right ) \, dx+4 \int e^{2 x} x^3 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^2 \log ^2\left (x^2\right ) \, dx+6 \int e^{2 x} x^2 \log ^2\left (x^2\right ) \, dx-6 \int e^x x^5 \log ^4\left (x^2\right ) \, dx+6 \int e^{2 x} x^5 \log ^4\left (x^2\right ) \, dx+8 \int e^{2 x} x^5 \log ^3\left (x^2\right ) \, dx-12 \int e^x x \log ^2\left (x^2\right ) \, dx-30 \int e^x x^4 \log ^4\left (x^2\right ) \, dx-48 \int e^x x^4 \log ^3\left (x^2\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.62, size = 47, normalized size = 1.62 \begin {gather*} e^{2 x}+x+2 e^x x^2 \left (-3+e^x x\right ) \log ^2\left (x^2\right )+x^4 \left (-3+e^x x\right )^2 \log ^4\left (x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 2*E^(2*x) + (-24*E^x*x + 8*E^(2*x)*x^2)*Log[x^2] + (E^x*(-12*x - 6*x^2) + E^(2*x)*(6*x^2 + 4*x^3
))*Log[x^2]^2 + (72*x^3 - 48*E^x*x^4 + 8*E^(2*x)*x^5)*Log[x^2]^3 + (36*x^3 + E^x*(-30*x^4 - 6*x^5) + E^(2*x)*(
6*x^5 + 2*x^6))*Log[x^2]^4,x]

[Out]

E^(2*x) + x + 2*E^x*x^2*(-3 + E^x*x)*Log[x^2]^2 + x^4*(-3 + E^x*x)^2*Log[x^2]^4

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fricas [B]  time = 0.60, size = 58, normalized size = 2.00 \begin {gather*} {\left (x^{6} e^{\left (2 \, x\right )} - 6 \, x^{5} e^{x} + 9 \, x^{4}\right )} \log \left (x^{2}\right )^{4} + 2 \, {\left (x^{3} e^{\left (2 \, x\right )} - 3 \, x^{2} e^{x}\right )} \log \left (x^{2}\right )^{2} + x + e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^6+6*x^5)*exp(x)^2+(-6*x^5-30*x^4)*exp(x)+36*x^3)*log(x^2)^4+(8*x^5*exp(x)^2-48*exp(x)*x^4+72*x
^3)*log(x^2)^3+((4*x^3+6*x^2)*exp(x)^2+(-6*x^2-12*x)*exp(x))*log(x^2)^2+(8*exp(x)^2*x^2-24*exp(x)*x)*log(x^2)+
2*exp(x)^2+1,x, algorithm="fricas")

[Out]

(x^6*e^(2*x) - 6*x^5*e^x + 9*x^4)*log(x^2)^4 + 2*(x^3*e^(2*x) - 3*x^2*e^x)*log(x^2)^2 + x + e^(2*x)

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giac [B]  time = 0.93, size = 259, normalized size = 8.93 \begin {gather*} -18 \, x^{4} \log \left (x^{2}\right )^{3} - {\left (4 \, x^{5} - 10 \, x^{4} + 20 \, x^{3} - 30 \, x^{2} + 30 \, x - 15\right )} e^{\left (2 \, x\right )} \log \left (x^{2}\right )^{3} + 48 \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} \log \left (x^{2}\right )^{3} + {\left (x^{6} e^{\left (2 \, x\right )} - 6 \, x^{5} e^{x} + 9 \, x^{4}\right )} \log \left (x^{2}\right )^{4} + {\left (18 \, x^{4} + {\left (4 \, x^{5} - 10 \, x^{4} + 20 \, x^{3} - 30 \, x^{2} + 30 \, x - 15\right )} e^{\left (2 \, x\right )} - 48 \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x}\right )} \log \left (x^{2}\right )^{3} - 2 \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} \log \left (x^{2}\right ) + 24 \, {\left (x - 1\right )} e^{x} \log \left (x^{2}\right ) + 2 \, {\left (x^{3} e^{\left (2 \, x\right )} - 3 \, x^{2} e^{x}\right )} \log \left (x^{2}\right )^{2} + 2 \, {\left ({\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} - 12 \, {\left (x - 1\right )} e^{x}\right )} \log \left (x^{2}\right ) + x + e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^6+6*x^5)*exp(x)^2+(-6*x^5-30*x^4)*exp(x)+36*x^3)*log(x^2)^4+(8*x^5*exp(x)^2-48*exp(x)*x^4+72*x
^3)*log(x^2)^3+((4*x^3+6*x^2)*exp(x)^2+(-6*x^2-12*x)*exp(x))*log(x^2)^2+(8*exp(x)^2*x^2-24*exp(x)*x)*log(x^2)+
2*exp(x)^2+1,x, algorithm="giac")

[Out]

-18*x^4*log(x^2)^3 - (4*x^5 - 10*x^4 + 20*x^3 - 30*x^2 + 30*x - 15)*e^(2*x)*log(x^2)^3 + 48*(x^4 - 4*x^3 + 12*
x^2 - 24*x + 24)*e^x*log(x^2)^3 + (x^6*e^(2*x) - 6*x^5*e^x + 9*x^4)*log(x^2)^4 + (18*x^4 + (4*x^5 - 10*x^4 + 2
0*x^3 - 30*x^2 + 30*x - 15)*e^(2*x) - 48*(x^4 - 4*x^3 + 12*x^2 - 24*x + 24)*e^x)*log(x^2)^3 - 2*(2*x^2 - 2*x +
1)*e^(2*x)*log(x^2) + 24*(x - 1)*e^x*log(x^2) + 2*(x^3*e^(2*x) - 3*x^2*e^x)*log(x^2)^2 + 2*((2*x^2 - 2*x + 1)
*e^(2*x) - 12*(x - 1)*e^x)*log(x^2) + x + e^(2*x)

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maple [C]  time = 0.57, size = 2156, normalized size = 74.34

method	result	size
risch	\(\text {Expression too large to display}\)	\(2156\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^6+6*x^5)*exp(x)^2+(-6*x^5-30*x^4)*exp(x)+36*x^3)*ln(x^2)^4+(8*x^5*exp(x)^2-48*exp(x)*x^4+72*x^3)*ln(
x^2)^3+((4*x^3+6*x^2)*exp(x)^2+(-6*x^2-12*x)*exp(x))*ln(x^2)^2+(8*exp(x)^2*x^2-24*exp(x)*x)*ln(x^2)+2*exp(x)^2
+1,x,method=_RETURNVERBOSE)

[Out]

x+exp(2*x)+4*I*Pi*csgn(I*x^2)^3*(1/2*exp(2*x)*x^2-1/2*x*exp(2*x)+1/4*exp(2*x))-1/2*Pi^2*csgn(I*x^2)^2*(csgn(I*
x)^2-2*csgn(I*x^2)*csgn(I*x)+csgn(I*x^2)^2)^2*(-3*exp(x)*x^2+exp(2*x)*x^3)+1/16*Pi^4*x^6*csgn(I*x^2)^12*exp(2*
x)+63/4*Pi^4*x^4*csgn(I*x)^6*csgn(I*x^2)^6-63/2*Pi^4*x^4*csgn(I*x)^5*csgn(I*x^2)^7+315/8*Pi^4*x^4*csgn(I*x)^4*
csgn(I*x^2)^8-63/2*Pi^4*x^4*csgn(I*x)^3*csgn(I*x^2)^9-3/8*Pi^4*x^5*csgn(I*x^2)^12*exp(x)+63/4*Pi^4*x^4*csgn(I*
x)^2*csgn(I*x^2)^10-9/2*Pi^4*x^4*csgn(I*x)*csgn(I*x^2)^11+9/16*Pi^4*x^4*csgn(I*x)^8*csgn(I*x^2)^4-9/2*Pi^4*x^4
*csgn(I*x)^7*csgn(I*x^2)^5-12*I*Pi*csgn(I*x^2)^3*(exp(x)*x-exp(x))+((8*x^2-8*x+4)*exp(2*x)+(-48*x+48)*exp(x))*
ln(x)+(-4*I*(Pi*x^3*csgn(I*x)^2*csgn(I*x^2)-2*Pi*x^3*csgn(I*x)*csgn(I*x^2)^2+Pi*x^3*csgn(I*x^2)^3-2*I*x^2+2*I*
x-I)*exp(2*x)+12*I*(Pi*x^2*csgn(I*x)^2*csgn(I*x^2)-2*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2+Pi*x^2*csgn(I*x^2)^3-4*I*x
+4*I)*exp(x))*ln(x)+(8*exp(2*x)*x^3-24*exp(x)*x^2)*ln(x)^2+(16*x^6*exp(2*x)-96*x^5*exp(x)+144*x^4)*ln(x)^4+(-6
*Pi^2*x^6*csgn(I*x)^4*csgn(I*x^2)^2*exp(2*x)+24*Pi^2*x^6*csgn(I*x)^3*csgn(I*x^2)^3*exp(2*x)-36*Pi^2*x^6*csgn(I
*x)^2*csgn(I*x^2)^4*exp(2*x)+24*Pi^2*x^6*csgn(I*x)*csgn(I*x^2)^5*exp(2*x)-6*Pi^2*x^6*csgn(I*x^2)^6*exp(2*x)+36
*Pi^2*x^5*csgn(I*x)^4*csgn(I*x^2)^2*exp(x)-144*Pi^2*x^5*csgn(I*x)^3*csgn(I*x^2)^3*exp(x)+216*Pi^2*x^5*csgn(I*x
)^2*csgn(I*x^2)^4*exp(x)-144*Pi^2*x^5*csgn(I*x)*csgn(I*x^2)^5*exp(x)+36*Pi^2*x^5*csgn(I*x^2)^6*exp(x)-54*Pi^2*
x^4*csgn(I*x)^4*csgn(I*x^2)^2+216*Pi^2*x^4*csgn(I*x)^3*csgn(I*x^2)^3-324*Pi^2*x^4*csgn(I*x)^2*csgn(I*x^2)^4+21
6*Pi^2*x^4*csgn(I*x)*csgn(I*x^2)^5-54*Pi^2*x^4*csgn(I*x^2)^6)*ln(x)^2-21/2*Pi^4*x^5*csgn(I*x)^6*csgn(I*x^2)^6*
exp(x)+21*Pi^4*x^5*csgn(I*x)^5*csgn(I*x^2)^7*exp(x)-105/4*Pi^4*x^5*csgn(I*x)^4*csgn(I*x^2)^8*exp(x)+21*Pi^4*x^
5*csgn(I*x)^3*csgn(I*x^2)^9*exp(x)-21/2*Pi^4*x^5*csgn(I*x)^2*csgn(I*x^2)^10*exp(x)+3*Pi^4*x^5*csgn(I*x)*csgn(I
*x^2)^11*exp(x)+1/16*Pi^4*x^6*csgn(I*x)^8*csgn(I*x^2)^4*exp(2*x)-1/2*Pi^4*x^6*csgn(I*x)^7*csgn(I*x^2)^5*exp(2*
x)-1/2*Pi^4*x^6*csgn(I*x)*csgn(I*x^2)^11*exp(2*x)-4*I*Pi*csgn(I*x^2)*(csgn(I*x)^2-2*csgn(I*x^2)*csgn(I*x)+csgn
(I*x^2)^2)*(1/2*exp(2*x)*x^2-1/2*x*exp(2*x)+1/4*exp(2*x)-3*exp(x)*x+3*exp(x))+24*I*Pi*csgn(I*x)*csgn(I*x^2)^2*
(exp(x)*x-exp(x))-12*I*Pi*csgn(I*x)^2*csgn(I*x^2)*(exp(x)*x-exp(x))-7/2*Pi^4*x^6*csgn(I*x)^5*csgn(I*x^2)^7*exp
(2*x)+9/16*Pi^4*x^4*csgn(I*x^2)^12+35/8*Pi^4*x^6*csgn(I*x)^4*csgn(I*x^2)^8*exp(2*x)-7/2*Pi^4*x^6*csgn(I*x)^3*c
sgn(I*x^2)^9*exp(2*x)+7/4*Pi^4*x^6*csgn(I*x)^2*csgn(I*x^2)^10*exp(2*x)-3/8*Pi^4*x^5*csgn(I*x)^8*csgn(I*x^2)^4*
exp(x)+3*Pi^4*x^5*csgn(I*x)^7*csgn(I*x^2)^5*exp(x)-8*I*Pi*csgn(I*x)*csgn(I*x^2)^2*(1/2*exp(2*x)*x^2-1/2*x*exp(
2*x)+1/4*exp(2*x))+4*I*Pi*csgn(I*x)^2*csgn(I*x^2)*(1/2*exp(2*x)*x^2-1/2*x*exp(2*x)+1/4*exp(2*x))-16*I*Pi*x^4*c
sgn(I*x^2)*(x^2*csgn(I*x)^2*exp(2*x)-2*x^2*csgn(I*x)*csgn(I*x^2)*exp(2*x)+x^2*csgn(I*x^2)^2*exp(2*x)-6*x*csgn(
I*x)^2*exp(x)+12*x*csgn(I*x)*csgn(I*x^2)*exp(x)-6*x*csgn(I*x^2)^2*exp(x)+9*csgn(I*x)^2-18*csgn(I*x^2)*csgn(I*x
)+9*csgn(I*x^2)^2)*ln(x)^3+I*Pi^3*x^4*csgn(I*x^2)^3*(x^2*csgn(I*x)^6*exp(2*x)-6*x^2*csgn(I*x)^5*csgn(I*x^2)*ex
p(2*x)+15*x^2*csgn(I*x)^4*csgn(I*x^2)^2*exp(2*x)-20*x^2*csgn(I*x)^3*csgn(I*x^2)^3*exp(2*x)+15*x^2*csgn(I*x)^2*
csgn(I*x^2)^4*exp(2*x)-6*x^2*csgn(I*x)*csgn(I*x^2)^5*exp(2*x)+x^2*csgn(I*x^2)^6*exp(2*x)-6*x*csgn(I*x)^6*exp(x
)+36*x*csgn(I*x)^5*csgn(I*x^2)*exp(x)-90*x*csgn(I*x)^4*csgn(I*x^2)^2*exp(x)+120*x*csgn(I*x)^3*csgn(I*x^2)^3*ex
p(x)-90*x*csgn(I*x)^2*csgn(I*x^2)^4*exp(x)+36*x*csgn(I*x)*csgn(I*x^2)^5*exp(x)-6*x*csgn(I*x^2)^6*exp(x)+9*csgn
(I*x)^6-54*csgn(I*x)^5*csgn(I*x^2)+135*csgn(I*x)^4*csgn(I*x^2)^2-180*csgn(I*x)^3*csgn(I*x^2)^3+135*csgn(I*x)^2
*csgn(I*x^2)^4-54*csgn(I*x)*csgn(I*x^2)^5+9*csgn(I*x^2)^6)*ln(x)+7/4*Pi^4*x^6*csgn(I*x)^6*csgn(I*x^2)^6*exp(2*
x)

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maxima [B]  time = 0.45, size = 61, normalized size = 2.10 \begin {gather*} 144 \, x^{4} \log \relax (x)^{4} + 8 \, {\left (2 \, x^{6} \log \relax (x)^{4} + x^{3} \log \relax (x)^{2}\right )} e^{\left (2 \, x\right )} - 24 \, {\left (4 \, x^{5} \log \relax (x)^{4} + x^{2} \log \relax (x)^{2}\right )} e^{x} + x + e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^6+6*x^5)*exp(x)^2+(-6*x^5-30*x^4)*exp(x)+36*x^3)*log(x^2)^4+(8*x^5*exp(x)^2-48*exp(x)*x^4+72*x
^3)*log(x^2)^3+((4*x^3+6*x^2)*exp(x)^2+(-6*x^2-12*x)*exp(x))*log(x^2)^2+(8*exp(x)^2*x^2-24*exp(x)*x)*log(x^2)+
2*exp(x)^2+1,x, algorithm="maxima")

[Out]

144*x^4*log(x)^4 + 8*(2*x^6*log(x)^4 + x^3*log(x)^2)*e^(2*x) - 24*(4*x^5*log(x)^4 + x^2*log(x)^2)*e^x + x + e^
(2*x)

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mupad [B]  time = 1.63, size = 59, normalized size = 2.03 \begin {gather*} \left (x^6\,{\mathrm {e}}^{2\,x}-6\,x^5\,{\mathrm {e}}^x+9\,x^4\right )\,{\ln \left (x^2\right )}^4+\left (2\,x^3\,{\mathrm {e}}^{2\,x}-6\,x^2\,{\mathrm {e}}^x\right )\,{\ln \left (x^2\right )}^2+x+{\mathrm {e}}^{2\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(2*x) + log(x^2)^4*(exp(2*x)*(6*x^5 + 2*x^6) - exp(x)*(30*x^4 + 6*x^5) + 36*x^3) + log(x^2)^3*(8*x^5*
exp(2*x) - 48*x^4*exp(x) + 72*x^3) + log(x^2)*(8*x^2*exp(2*x) - 24*x*exp(x)) + log(x^2)^2*(exp(2*x)*(6*x^2 + 4
*x^3) - exp(x)*(12*x + 6*x^2)) + 1,x)

[Out]

x + exp(2*x) + log(x^2)^4*(x^6*exp(2*x) - 6*x^5*exp(x) + 9*x^4) - log(x^2)^2*(6*x^2*exp(x) - 2*x^3*exp(2*x))

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sympy [B]  time = 0.54, size = 70, normalized size = 2.41 \begin {gather*} 9 x^{4} \log {\left (x^{2} \right )}^{4} + x + \left (- 6 x^{5} \log {\left (x^{2} \right )}^{4} - 6 x^{2} \log {\left (x^{2} \right )}^{2}\right ) e^{x} + \left (x^{6} \log {\left (x^{2} \right )}^{4} + 2 x^{3} \log {\left (x^{2} \right )}^{2} + 1\right ) e^{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**6+6*x**5)*exp(x)**2+(-6*x**5-30*x**4)*exp(x)+36*x**3)*ln(x**2)**4+(8*x**5*exp(x)**2-48*exp(x)
*x**4+72*x**3)*ln(x**2)**3+((4*x**3+6*x**2)*exp(x)**2+(-6*x**2-12*x)*exp(x))*ln(x**2)**2+(8*exp(x)**2*x**2-24*
exp(x)*x)*ln(x**2)+2*exp(x)**2+1,x)

[Out]

9*x**4*log(x**2)**4 + x + (-6*x**5*log(x**2)**4 - 6*x**2*log(x**2)**2)*exp(x) + (x**6*log(x**2)**4 + 2*x**3*lo
g(x**2)**2 + 1)*exp(2*x)

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