3.67.11 \(\int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} (-10+2 x^2)+e^{4+x} (20 x+4 x^2)+e^4 (-x-10 x^2-2 x^3)+(8 x^3+e^{4+3 x} (-4 x+4 x^2)+e^4 (-20 x^2-2 x^3)+e^{2 x} (8 x+e^4 (-18 x-4 x^3))+e^x (-16 x^2+e^4 (20 x+20 x^2+4 x^3))) \log (x)+(-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5) \log ^2(x)}{2 x+(-8 e^{2 x} x+16 e^x x^2-8 x^3) \log (x)+(8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5) \log ^2(x)} \, dx\)

Optimal. Leaf size=35 \[ -x+\frac {e^4 \left (-5+e^{2 x}-x\right )}{2-4 \left (-e^x+x\right )^2 \log (x)} \]

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Rubi [F]  time = 21.80, 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 e^{4+4 x}-2 x-4 e^{4+3 x} x+e^{4+2 x} \left (-10+2 x^2\right )+e^{4+x} \left (20 x+4 x^2\right )+e^4 \left (-x-10 x^2-2 x^3\right )+\left (8 x^3+e^{4+3 x} \left (-4 x+4 x^2\right )+e^4 \left (-20 x^2-2 x^3\right )+e^{2 x} \left (8 x+e^4 \left (-18 x-4 x^3\right )\right )+e^x \left (-16 x^2+e^4 \left (20 x+20 x^2+4 x^3\right )\right )\right ) \log (x)+\left (-8 e^{4 x} x+32 e^{3 x} x^2-48 e^{2 x} x^3+32 e^x x^4-8 x^5\right ) \log ^2(x)}{2 x+\left (-8 e^{2 x} x+16 e^x x^2-8 x^3\right ) \log (x)+\left (8 e^{4 x} x-32 e^{3 x} x^2+48 e^{2 x} x^3-32 e^x x^4+8 x^5\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2*E^(4 + 4*x) - 2*x - 4*E^(4 + 3*x)*x + E^(4 + 2*x)*(-10 + 2*x^2) + E^(4 + x)*(20*x + 4*x^2) + E^4*(-x -
10*x^2 - 2*x^3) + (8*x^3 + E^(4 + 3*x)*(-4*x + 4*x^2) + E^4*(-20*x^2 - 2*x^3) + E^(2*x)*(8*x + E^4*(-18*x - 4*
x^3)) + E^x*(-16*x^2 + E^4*(20*x + 20*x^2 + 4*x^3)))*Log[x] + (-8*E^(4*x)*x + 32*E^(3*x)*x^2 - 48*E^(2*x)*x^3
+ 32*E^x*x^4 - 8*x^5)*Log[x]^2)/(2*x + (-8*E^(2*x)*x + 16*E^x*x^2 - 8*x^3)*Log[x] + (8*E^(4*x)*x - 32*E^(3*x)*
x^2 + 48*E^(2*x)*x^3 - 32*E^x*x^4 + 8*x^5)*Log[x]^2),x]

[Out]

-x - E^4/(4*Log[x]) - 5*E^4*Defer[Int][(1 - 2*(E^x - x)^2*Log[x])^(-2), x] - E^4*Defer[Int][E^x/(1 - 2*(E^x -
x)^2*Log[x])^2, x] - 2*E^4*Defer[Int][x/(1 - 2*(E^x - x)^2*Log[x])^2, x] + 3*E^4*Defer[Int][(E^x*x)/(1 - 2*(E^
x - x)^2*Log[x])^2, x] + (E^4*Defer[Int][1/(x*Log[x]^2*(1 - 2*(E^x - x)^2*Log[x])^2), x])/4 + E^4*Defer[Int][E
^x/(Log[x]*(1 - 2*(E^x - x)^2*Log[x])^2), x] - (5*E^4*Defer[Int][1/(x*Log[x]*(1 - 2*(E^x - x)^2*Log[x])^2), x]
)/2 - (E^4*Defer[Int][x/(Log[x]*(1 - 2*(E^x - x)^2*Log[x])^2), x])/2 + 10*E^4*Defer[Int][(E^x*Log[x])/(1 - 2*(
E^x - x)^2*Log[x])^2, x] - 10*E^4*Defer[Int][(x*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x] - 8*E^4*Defer[Int][(E
^x*x*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x] + 8*E^4*Defer[Int][(x^2*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x]
- 4*E^4*Defer[Int][(E^x*x^2*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x] + 4*E^4*Defer[Int][(x^3*Log[x])/(1 - 2*(
E^x - x)^2*Log[x])^2, x] + 2*E^4*Defer[Int][(E^x*x^3*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x] - 2*E^4*Defer[In
t][(x^4*Log[x])/(1 - 2*(E^x - x)^2*Log[x])^2, x] - (9*E^4*Defer[Int][(-1 + 2*(E^x - x)^2*Log[x])^(-1), x])/2 -
E^4*Defer[Int][E^x/(-1 + 2*(E^x - x)^2*Log[x]), x] - 2*E^4*Defer[Int][x/(-1 + 2*(E^x - x)^2*Log[x]), x] + E^4
*Defer[Int][(E^x*x)/(-1 + 2*(E^x - x)^2*Log[x]), x] + E^4*Defer[Int][x^2/(-1 + 2*(E^x - x)^2*Log[x]), x] + (E^
4*Defer[Int][1/(x*Log[x]^2*(-1 + 2*(E^x - x)^2*Log[x])), x])/2 + E^4*Defer[Int][E^x/(Log[x]*(-1 + 2*(E^x - x)^
2*Log[x])), x] - (5*E^4*Defer[Int][1/(x*Log[x]*(-1 + 2*(E^x - x)^2*Log[x])), x])/2 - (E^4*Defer[Int][x/(Log[x]
*(-1 + 2*(E^x - x)^2*Log[x])), x])/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+4 e^{4+x} x (5+x)+2 e^{4+2 x} \left (-5+x^2\right )-e^4 x \left (1+10 x+2 x^2\right )-2 x \left (-4 e^{2 x}-2 e^{4+3 x} (-1+x)+8 e^x x-4 x^2+e^4 x (10+x)-2 e^{4+x} \left (5+5 x+x^2\right )+e^{4+2 x} \left (9+2 x^2\right )\right ) \log (x)-8 \left (e^x-x\right )^4 x \log ^2(x)}{2 x \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {2 e^{4+4 x}-2 x-4 e^{4+3 x} x+4 e^{4+x} x (5+x)+2 e^{4+2 x} \left (-5+x^2\right )-e^4 x \left (1+10 x+2 x^2\right )-2 x \left (-4 e^{2 x}-2 e^{4+3 x} (-1+x)+8 e^x x-4 x^2+e^4 x (10+x)-2 e^{4+x} \left (5+5 x+x^2\right )+e^{4+2 x} \left (9+2 x^2\right )\right ) \log (x)-8 \left (e^x-x\right )^4 x \log ^2(x)}{x \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {e^4-4 x \log ^2(x)}{2 x \log ^2(x)}+\frac {e^4 \left (1-5 \log (x)+2 e^x x \log (x)-x^2 \log (x)-9 x \log ^2(x)-2 e^x x \log ^2(x)-4 x^2 \log ^2(x)+2 e^x x^2 \log ^2(x)+2 x^3 \log ^2(x)\right )}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )}-\frac {e^4 \left (-1+10 \log (x)-4 e^x x \log (x)+2 x^2 \log (x)+20 x \log ^2(x)+4 e^x x \log ^2(x)+8 x^2 \log ^2(x)-12 e^x x^2 \log ^2(x)-40 e^x x \log ^3(x)+40 x^2 \log ^3(x)+32 e^x x^2 \log ^3(x)-32 x^3 \log ^3(x)+16 e^x x^3 \log ^3(x)-16 x^4 \log ^3(x)-8 e^x x^4 \log ^3(x)+8 x^5 \log ^3(x)\right )}{2 x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2}\right ) \, dx\\ &=\frac {1}{4} \int \frac {e^4-4 x \log ^2(x)}{x \log ^2(x)} \, dx-\frac {1}{4} e^4 \int \frac {-1+10 \log (x)-4 e^x x \log (x)+2 x^2 \log (x)+20 x \log ^2(x)+4 e^x x \log ^2(x)+8 x^2 \log ^2(x)-12 e^x x^2 \log ^2(x)-40 e^x x \log ^3(x)+40 x^2 \log ^3(x)+32 e^x x^2 \log ^3(x)-32 x^3 \log ^3(x)+16 e^x x^3 \log ^3(x)-16 x^4 \log ^3(x)-8 e^x x^4 \log ^3(x)+8 x^5 \log ^3(x)}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {1-5 \log (x)+2 e^x x \log (x)-x^2 \log (x)-9 x \log ^2(x)-2 e^x x \log ^2(x)-4 x^2 \log ^2(x)+2 e^x x^2 \log ^2(x)+2 x^3 \log ^2(x)}{x \log ^2(x) \left (-1+2 e^{2 x} \log (x)-4 e^x x \log (x)+2 x^2 \log (x)\right )} \, dx\\ &=\frac {1}{4} \int \left (-4+\frac {e^4}{x \log ^2(x)}\right ) \, dx-\frac {1}{4} e^4 \int \frac {-1+2 \left (5-2 e^x x+x^2\right ) \log (x)-4 x \left (-5-2 x+e^x (-1+3 x)\right ) \log ^2(x)-8 \left (e^x-x\right ) x \left (5-4 x-2 x^2+x^3\right ) \log ^3(x)}{x \log ^2(x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )^2} \, dx+\frac {1}{2} e^4 \int \frac {-1-\left (-5+2 e^x x-x^2\right ) \log (x)-x \left (-9+2 e^x (-1+x)-4 x+2 x^2\right ) \log ^2(x)}{x \log ^2(x) \left (1-2 \left (e^x-x\right )^2 \log (x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 40, normalized size = 1.14 \begin {gather*} \frac {1}{2} \left (-2 x-\frac {e^4 \left (-5+e^{2 x}-x\right )}{-1+2 \left (e^x-x\right )^2 \log (x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*E^(4 + 4*x) - 2*x - 4*E^(4 + 3*x)*x + E^(4 + 2*x)*(-10 + 2*x^2) + E^(4 + x)*(20*x + 4*x^2) + E^4*
(-x - 10*x^2 - 2*x^3) + (8*x^3 + E^(4 + 3*x)*(-4*x + 4*x^2) + E^4*(-20*x^2 - 2*x^3) + E^(2*x)*(8*x + E^4*(-18*
x - 4*x^3)) + E^x*(-16*x^2 + E^4*(20*x + 20*x^2 + 4*x^3)))*Log[x] + (-8*E^(4*x)*x + 32*E^(3*x)*x^2 - 48*E^(2*x
)*x^3 + 32*E^x*x^4 - 8*x^5)*Log[x]^2)/(2*x + (-8*E^(2*x)*x + 16*E^x*x^2 - 8*x^3)*Log[x] + (8*E^(4*x)*x - 32*E^
(3*x)*x^2 + 48*E^(2*x)*x^3 - 32*E^x*x^4 + 8*x^5)*Log[x]^2),x]

[Out]

(-2*x - (E^4*(-5 + E^(2*x) - x))/(-1 + 2*(E^x - x)^2*Log[x]))/2

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fricas [B]  time = 0.57, size = 81, normalized size = 2.31 \begin {gather*} \frac {{\left (x + 5\right )} e^{12} + 2 \, x e^{8} - 4 \, {\left (x^{3} e^{8} - 2 \, x^{2} e^{\left (x + 8\right )} + x e^{\left (2 \, x + 8\right )}\right )} \log \relax (x) - e^{\left (2 \, x + 12\right )}}{2 \, {\left (2 \, {\left (x^{2} e^{8} - 2 \, x e^{\left (x + 8\right )} + e^{\left (2 \, x + 8\right )}\right )} \log \relax (x) - e^{8}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x*exp(x)^4+32*x^2*exp(x)^3-48*exp(x)^2*x^3+32*exp(x)*x^4-8*x^5)*log(x)^2+((4*x^2-4*x)*exp(4)*ex
p(x)^3+((-4*x^3-18*x)*exp(4)+8*x)*exp(x)^2+((4*x^3+20*x^2+20*x)*exp(4)-16*x^2)*exp(x)+(-2*x^3-20*x^2)*exp(4)+8
*x^3)*log(x)+2*exp(4)*exp(x)^4-4*x*exp(4)*exp(x)^3+(2*x^2-10)*exp(4)*exp(x)^2+(4*x^2+20*x)*exp(4)*exp(x)+(-2*x
^3-10*x^2-x)*exp(4)-2*x)/((8*x*exp(x)^4-32*x^2*exp(x)^3+48*exp(x)^2*x^3-32*exp(x)*x^4+8*x^5)*log(x)^2+(-8*x*ex
p(x)^2+16*exp(x)*x^2-8*x^3)*log(x)+2*x),x, algorithm="fricas")

[Out]

1/2*((x + 5)*e^12 + 2*x*e^8 - 4*(x^3*e^8 - 2*x^2*e^(x + 8) + x*e^(2*x + 8))*log(x) - e^(2*x + 12))/(2*(x^2*e^8
- 2*x*e^(x + 8) + e^(2*x + 8))*log(x) - e^8)

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giac [B]  time = 2.97, size = 842, normalized size = 24.06 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x*exp(x)^4+32*x^2*exp(x)^3-48*exp(x)^2*x^3+32*exp(x)*x^4-8*x^5)*log(x)^2+((4*x^2-4*x)*exp(4)*ex
p(x)^3+((-4*x^3-18*x)*exp(4)+8*x)*exp(x)^2+((4*x^3+20*x^2+20*x)*exp(4)-16*x^2)*exp(x)+(-2*x^3-20*x^2)*exp(4)+8
*x^3)*log(x)+2*exp(4)*exp(x)^4-4*x*exp(4)*exp(x)^3+(2*x^2-10)*exp(4)*exp(x)^2+(4*x^2+20*x)*exp(4)*exp(x)+(-2*x
^3-10*x^2-x)*exp(4)-2*x)/((8*x*exp(x)^4-32*x^2*exp(x)^3+48*exp(x)^2*x^3-32*exp(x)*x^4+8*x^5)*log(x)^2+(-8*x*ex
p(x)^2+16*exp(x)*x^2-8*x^3)*log(x)+2*x),x, algorithm="giac")

[Out]

-1/2*(32*x^8*log(x)^5 - 32*x^7*e^x*log(x)^5 - 32*x^7*log(x)^5 + 32*x^6*e^x*log(x)^5 + 32*x^7*log(x)^4 + 8*x^6*
e^4*log(x)^4 - 64*x^6*e^x*log(x)^4 + 8*x^6*e^4*log(x)^3 - 80*x^6*log(x)^4 + 72*x^5*e^4*log(x)^4 + 32*x^5*e^(2*
x)*log(x)^4 - 8*x^5*e^(x + 4)*log(x)^4 + 160*x^5*e^x*log(x)^4 + 24*x^5*e^4*log(x)^3 - 8*x^5*e^(x + 4)*log(x)^3
+ 64*x^5*log(x)^4 - 80*x^4*e^4*log(x)^4 - 64*x^4*e^(2*x)*log(x)^4 - 72*x^4*e^(x + 4)*log(x)^4 - 96*x^4*e^x*lo
g(x)^4 - 24*x^5*log(x)^3 - 56*x^4*e^4*log(x)^3 + 8*x^4*e^(2*x + 4)*log(x)^3 - 32*x^4*e^(x + 4)*log(x)^3 + 32*x
^4*e^x*log(x)^3 + 32*x^3*e^(2*x)*log(x)^4 + 80*x^3*e^(x + 4)*log(x)^4 + 4*x^4*e^4*log(x)^2 + 24*x^4*log(x)^3 +
108*x^3*e^4*log(x)^3 - 16*x^3*e^(2*x)*log(x)^3 - 16*x^3*e^(2*x + 4)*log(x)^3 + 36*x^3*e^(x + 4)*log(x)^3 - 8*
x^3*e^x*log(x)^3 - 16*x^4*log(x)^2 + 26*x^3*e^4*log(x)^2 + 32*x^3*e^x*log(x)^2 - 24*x^3*log(x)^3 - 40*x^2*e^4*
log(x)^3 + 8*x^2*e^(2*x + 4)*log(x)^3 + 4*x^2*e^(x + 4)*log(x)^3 + 8*x^2*e^x*log(x)^3 + 2*x^3*e^4*log(x) + 42*
x^2*e^4*log(x)^2 - 16*x^2*e^(2*x)*log(x)^2 - 4*x^2*e^(2*x + 4)*log(x)^2 - 4*x^3*log(x) + 14*x^2*e^4*log(x) + 8
*x^2*e^x*log(x) + 4*x^2*log(x)^2 + 8*x^2*log(x) + 21*x*e^4*log(x) - 4*x*e^(2*x)*log(x) - 4*x*e^(2*x + 4)*log(x
) + x*e^4 + 2*x*log(x) + 2*x + 5*e^4 - e^(2*x + 4))/(16*x^6*log(x)^4 - 32*x^5*e^x*log(x)^4 - 32*x^5*log(x)^4 +
16*x^4*e^(2*x)*log(x)^4 + 64*x^4*e^x*log(x)^4 + 16*x^4*log(x)^4 - 32*x^3*e^(2*x)*log(x)^4 - 32*x^3*e^x*log(x)
^4 - 16*x^4*log(x)^3 + 16*x^3*e^x*log(x)^3 + 16*x^2*e^(2*x)*log(x)^4 + 16*x^3*log(x)^3 - 8*x^2*e^(2*x)*log(x)^
3 - 8*x^3*log(x)^2 + 16*x^2*e^x*log(x)^2 - 8*x^2*log(x)^3 + 4*x^2*log(x)^2 - 8*x*e^(2*x)*log(x)^2 - 2*x^2*log(
x) + 4*x*e^x*log(x) + 4*x*log(x) - 2*e^(2*x)*log(x) + 1)

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maple [A]  time = 0.09, size = 44, normalized size = 1.26

method	result	size
risch	\(-x +\frac {\left (5+x -{\mathrm e}^{2 x}\right ) {\mathrm e}^{4}}{4 \ln \relax (x ) {\mathrm e}^{2 x}-8 x \,{\mathrm e}^{x} \ln \relax (x )+4 x^{2} \ln \relax (x )-2}\)	\(44\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-8*x*exp(x)^4+32*x^2*exp(x)^3-48*exp(x)^2*x^3+32*exp(x)*x^4-8*x^5)*ln(x)^2+((4*x^2-4*x)*exp(4)*exp(x)^3+
((-4*x^3-18*x)*exp(4)+8*x)*exp(x)^2+((4*x^3+20*x^2+20*x)*exp(4)-16*x^2)*exp(x)+(-2*x^3-20*x^2)*exp(4)+8*x^3)*l
n(x)+2*exp(4)*exp(x)^4-4*x*exp(4)*exp(x)^3+(2*x^2-10)*exp(4)*exp(x)^2+(4*x^2+20*x)*exp(4)*exp(x)+(-2*x^3-10*x^
2-x)*exp(4)-2*x)/((8*x*exp(x)^4-32*x^2*exp(x)^3+48*exp(x)^2*x^3-32*exp(x)*x^4+8*x^5)*ln(x)^2+(-8*x*exp(x)^2+16
*exp(x)*x^2-8*x^3)*ln(x)+2*x),x,method=_RETURNVERBOSE)

[Out]

-x+1/2*(5+x-exp(2*x))*exp(4)/(2*ln(x)*exp(2*x)-4*x*exp(x)*ln(x)+2*x^2*ln(x)-1)

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maxima [B]  time = 0.51, size = 69, normalized size = 1.97 \begin {gather*} -\frac {4 \, x^{3} \log \relax (x) - 8 \, x^{2} e^{x} \log \relax (x) - x {\left (e^{4} + 2\right )} + {\left (4 \, x \log \relax (x) + e^{4}\right )} e^{\left (2 \, x\right )} - 5 \, e^{4}}{2 \, {\left (2 \, x^{2} \log \relax (x) - 4 \, x e^{x} \log \relax (x) + 2 \, e^{\left (2 \, x\right )} \log \relax (x) - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x*exp(x)^4+32*x^2*exp(x)^3-48*exp(x)^2*x^3+32*exp(x)*x^4-8*x^5)*log(x)^2+((4*x^2-4*x)*exp(4)*ex
p(x)^3+((-4*x^3-18*x)*exp(4)+8*x)*exp(x)^2+((4*x^3+20*x^2+20*x)*exp(4)-16*x^2)*exp(x)+(-2*x^3-20*x^2)*exp(4)+8
*x^3)*log(x)+2*exp(4)*exp(x)^4-4*x*exp(4)*exp(x)^3+(2*x^2-10)*exp(4)*exp(x)^2+(4*x^2+20*x)*exp(4)*exp(x)+(-2*x
^3-10*x^2-x)*exp(4)-2*x)/((8*x*exp(x)^4-32*x^2*exp(x)^3+48*exp(x)^2*x^3-32*exp(x)*x^4+8*x^5)*log(x)^2+(-8*x*ex
p(x)^2+16*exp(x)*x^2-8*x^3)*log(x)+2*x),x, algorithm="maxima")

[Out]

-1/2*(4*x^3*log(x) - 8*x^2*e^x*log(x) - x*(e^4 + 2) + (4*x*log(x) + e^4)*e^(2*x) - 5*e^4)/(2*x^2*log(x) - 4*x*
e^x*log(x) + 2*e^(2*x)*log(x) - 1)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\left (8\,x\,{\mathrm {e}}^{4\,x}-32\,x^4\,{\mathrm {e}}^x-32\,x^2\,{\mathrm {e}}^{3\,x}+48\,x^3\,{\mathrm {e}}^{2\,x}+8\,x^5\right )\,{\ln \relax (x)}^2+\left ({\mathrm {e}}^4\,\left (2\,x^3+20\,x^2\right )-{\mathrm {e}}^x\,\left ({\mathrm {e}}^4\,\left (4\,x^3+20\,x^2+20\,x\right )-16\,x^2\right )-{\mathrm {e}}^{2\,x}\,\left (8\,x-{\mathrm {e}}^4\,\left (4\,x^3+18\,x\right )\right )-8\,x^3+{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4\,\left (4\,x-4\,x^2\right )\right )\,\ln \relax (x)+2\,x-2\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^4+{\mathrm {e}}^4\,\left (2\,x^3+10\,x^2+x\right )-{\mathrm {e}}^4\,{\mathrm {e}}^x\,\left (4\,x^2+20\,x\right )+4\,x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4\,\left (2\,x^2-10\right )}{\left (8\,x\,{\mathrm {e}}^{4\,x}-32\,x^4\,{\mathrm {e}}^x-32\,x^2\,{\mathrm {e}}^{3\,x}+48\,x^3\,{\mathrm {e}}^{2\,x}+8\,x^5\right )\,{\ln \relax (x)}^2+\left (16\,x^2\,{\mathrm {e}}^x-8\,x\,{\mathrm {e}}^{2\,x}-8\,x^3\right )\,\ln \relax (x)+2\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 2*exp(4*x)*exp(4) + exp(4)*(x + 10*x^2 + 2*x^3) - log(x)*(exp(2*x)*(8*x - exp(4)*(18*x + 4*x^3)) +
exp(x)*(exp(4)*(20*x + 20*x^2 + 4*x^3) - 16*x^2) - exp(4)*(20*x^2 + 2*x^3) + 8*x^3 - exp(3*x)*exp(4)*(4*x - 4
*x^2)) + log(x)^2*(8*x*exp(4*x) - 32*x^4*exp(x) - 32*x^2*exp(3*x) + 48*x^3*exp(2*x) + 8*x^5) - exp(4)*exp(x)*(
20*x + 4*x^2) + 4*x*exp(3*x)*exp(4) - exp(2*x)*exp(4)*(2*x^2 - 10))/(2*x - log(x)*(8*x*exp(2*x) - 16*x^2*exp(x
) + 8*x^3) + log(x)^2*(8*x*exp(4*x) - 32*x^4*exp(x) - 32*x^2*exp(3*x) + 48*x^3*exp(2*x) + 8*x^5)),x)

[Out]

int(-(2*x - 2*exp(4*x)*exp(4) + exp(4)*(x + 10*x^2 + 2*x^3) - log(x)*(exp(2*x)*(8*x - exp(4)*(18*x + 4*x^3)) +
exp(x)*(exp(4)*(20*x + 20*x^2 + 4*x^3) - 16*x^2) - exp(4)*(20*x^2 + 2*x^3) + 8*x^3 - exp(3*x)*exp(4)*(4*x - 4
*x^2)) + log(x)^2*(8*x*exp(4*x) - 32*x^4*exp(x) - 32*x^2*exp(3*x) + 48*x^3*exp(2*x) + 8*x^5) - exp(4)*exp(x)*(
20*x + 4*x^2) + 4*x*exp(3*x)*exp(4) - exp(2*x)*exp(4)*(2*x^2 - 10))/(2*x - log(x)*(8*x*exp(2*x) - 16*x^2*exp(x
) + 8*x^3) + log(x)^2*(8*x*exp(4*x) - 32*x^4*exp(x) - 32*x^2*exp(3*x) + 48*x^3*exp(2*x) + 8*x^5)), x)

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sympy [B]  time = 0.58, size = 95, normalized size = 2.71 \begin {gather*} - x - \frac {e^{4}}{4 \log {\relax (x )}} + \frac {2 x^{2} e^{4} \log {\relax (x )} - 4 x e^{4} e^{x} \log {\relax (x )} + 2 x e^{4} \log {\relax (x )} + 10 e^{4} \log {\relax (x )} - e^{4}}{8 x^{2} \log {\relax (x )}^{2} - 16 x e^{x} \log {\relax (x )}^{2} + 8 e^{2 x} \log {\relax (x )}^{2} - 4 \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x*exp(x)**4+32*x**2*exp(x)**3-48*exp(x)**2*x**3+32*exp(x)*x**4-8*x**5)*ln(x)**2+((4*x**2-4*x)*e
xp(4)*exp(x)**3+((-4*x**3-18*x)*exp(4)+8*x)*exp(x)**2+((4*x**3+20*x**2+20*x)*exp(4)-16*x**2)*exp(x)+(-2*x**3-2
0*x**2)*exp(4)+8*x**3)*ln(x)+2*exp(4)*exp(x)**4-4*x*exp(4)*exp(x)**3+(2*x**2-10)*exp(4)*exp(x)**2+(4*x**2+20*x
)*exp(4)*exp(x)+(-2*x**3-10*x**2-x)*exp(4)-2*x)/((8*x*exp(x)**4-32*x**2*exp(x)**3+48*exp(x)**2*x**3-32*exp(x)*
x**4+8*x**5)*ln(x)**2+(-8*x*exp(x)**2+16*exp(x)*x**2-8*x**3)*ln(x)+2*x),x)

[Out]

-x - exp(4)/(4*log(x)) + (2*x**2*exp(4)*log(x) - 4*x*exp(4)*exp(x)*log(x) + 2*x*exp(4)*log(x) + 10*exp(4)*log(
x) - exp(4))/(8*x**2*log(x)**2 - 16*x*exp(x)*log(x)**2 + 8*exp(2*x)*log(x)**2 - 4*log(x))

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