3.51.74 \(\int \frac {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+(147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2) \log (x)+(e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2) \log (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2)}{e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2} \, dx\)

Optimal. Leaf size=30 \[ (-2+\log (x)) \log \left (x \left (e^x+(x-4 x (2-i \pi -\log (3)))^2\right )\right ) \]

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Rubi [F]  time = 3.86, 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 {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(-2 - 2*x) - 294*x^2 + 336*x^2*(I*Pi + Log[3]) - 96*x^2*(I*Pi + Log[3])^2 + (147*x^2 + E^x*(1 + x) -
168*x^2*(I*Pi + Log[3]) + 48*x^2*(I*Pi + Log[3])^2)*Log[x] + (E^x + 49*x^2 - 56*x^2*(I*Pi + Log[3]) + 16*x^2*(
I*Pi + Log[3])^2)*Log[E^x*x + 49*x^3 - 56*x^3*(I*Pi + Log[3]) + 16*x^3*(I*Pi + Log[3])^2])/(E^x*x + 49*x^3 - 5
6*x^3*(I*Pi + Log[3]) + 16*x^3*(I*Pi + Log[3])^2),x]

[Out]

-3*x + (2 - Log[x])^2/2 + x*Log[x] + 2*(7*I + 4*Pi - (4*I)*Log[3])^2*Log[x]*Defer[Int][x/(-E^x - 49*x^2*(1 + (
-16*Pi^2 + 8*Log[3]*(-7 + Log[9]) + (8*I)*Pi*(-7 + Log[81]))/49)), x] + 2*(7*I + 4*Pi - (4*I)*Log[3])^2*Defer[
Int][x^2/(-E^x - 49*x^2*(1 + (-16*Pi^2 + 8*Log[3]*(-7 + Log[9]) + (8*I)*Pi*(-7 + Log[81]))/49)), x] + 4*(7*I +
4*Pi - (4*I)*Log[3])^2*Defer[Int][x/(E^x + 49*x^2*(1 + (-16*Pi^2 + 8*Log[3]*(-7 + Log[9]) + (8*I)*Pi*(-7 + Lo
g[81]))/49)), x] + (7*I + 4*Pi - (4*I)*Log[3])^2*Log[x]*Defer[Int][x^2/(E^x + 49*x^2*(1 + (-16*Pi^2 + 8*Log[3]
*(-7 + Log[9]) + (8*I)*Pi*(-7 + Log[81]))/49)), x] + Defer[Int][Log[E^x*x - x^3*(7*I + 4*Pi - (4*I)*Log[3])^2]
/x, x] - 2*(7*I + 4*Pi - (4*I)*Log[3])^2*Defer[Int][Defer[Int][-(x/(E^x + x^2*(49 - 16*Pi^2 + 8*Log[3]*(-7 + L
og[9]) + (8*I)*Pi*(-7 + Log[81])))), x]/x, x] - (7*I + 4*Pi - (4*I)*Log[3])^2*Defer[Int][Defer[Int][x^2/(E^x +
x^2*(49 - 16*Pi^2 + 8*Log[3]*(-7 + Log[9]) + (8*I)*Pi*(-7 + Log[81]))), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+16 x^3 (i \pi +\log (3))^2+x^3 (49-56 (i \pi +\log (3)))} \, dx\\ &=\int \frac {e^x (-2-2 x)-294 x^2+336 x^2 (i \pi +\log (3))-96 x^2 (i \pi +\log (3))^2+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {e^x (-2-2 x)-96 x^2 (i \pi +\log (3))^2+x^2 (-294+336 (i \pi +\log (3)))+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {e^x (-2-2 x)+x^2 \left (-294+336 (i \pi +\log (3))-96 (i \pi +\log (3))^2\right )+\left (147 x^2+e^x (1+x)-168 x^2 (i \pi +\log (3))+48 x^2 (i \pi +\log (3))^2\right ) \log (x)+\left (e^x+49 x^2-56 x^2 (i \pi +\log (3))+16 x^2 (i \pi +\log (3))^2\right ) \log \left (e^x x+49 x^3-56 x^3 (i \pi +\log (3))+16 x^3 (i \pi +\log (3))^2\right )}{e^x x+x^3 \left (49-56 (i \pi +\log (3))+16 (i \pi +\log (3))^2\right )} \, dx\\ &=\int \frac {-2 e^x (1+x)+6 x^2 (7 i+4 \pi -4 i \log (3))^2+\left (e^x (1+x)-3 x^2 (7 i+4 \pi -4 i \log (3))^2\right ) \log (x)+\left (e^x-x^2 (7 i+4 \pi -4 i \log (3))^2\right ) \log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2} \, dx\\ &=\int \left (\frac {(2-x) x (7 i+4 \pi -4 i \log (3))^2 (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {-2-2 x+\log (x)+x \log (x)+\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x}\right ) \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \frac {(2-x) x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {-2-2 x+\log (x)+x \log (x)+\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \left (\frac {2 x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x^2 (-2+\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\int \left (\frac {(1+x) (-2+\log (x))}{x}+\frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x}\right ) \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \frac {x^2 (-2+\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x (2-\log (x))}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {(1+x) (-2+\log (x))}{x} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=(7 i+4 \pi -4 i \log (3))^2 \int \left (\frac {2 x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x^2 \log (x)}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \left (\frac {2 x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}+\frac {x \log (x)}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )}\right ) \, dx+\int (-2+\log (x)) \, dx+\int \frac {-2+\log (x)}{x} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-2 x+\frac {1}{2} (2-\log (x))^2+(7 i+4 \pi -4 i \log (3))^2 \int \frac {x^2 \log (x)}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x \log (x)}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \log (x) \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-3 x+\frac {1}{2} (2-\log (x))^2+x \log (x)-(7 i+4 \pi -4 i \log (3))^2 \int \frac {\int \frac {x^2}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx-\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {\int -\frac {x}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left ((7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x^2}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ &=-3 x+\frac {1}{2} (2-\log (x))^2+x \log (x)-(7 i+4 \pi -4 i \log (3))^2 \int \frac {\int \frac {x^2}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x^2}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {\int \frac {x}{e^x+x^2 \left (49-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )} \, dx}{x} \, dx+\left (4 (7 i+4 \pi -4 i \log (3))^2\right ) \int \frac {x}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left ((7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x^2}{e^x+49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\left (2 (7 i+4 \pi -4 i \log (3))^2 \log (x)\right ) \int \frac {x}{-e^x-49 x^2 \left (1+\frac {1}{49} \left (-16 \pi ^2+8 \log (3) (-7+\log (9))+8 i \pi (-7+\log (81))\right )\right )} \, dx+\int \frac {\log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.21, size = 216, normalized size = 7.20 \begin {gather*} 2 i \tan ^{-1}\left (\frac {8 \pi x^2 (-7+4 \log (3))}{-e^x-49 x^2+16 \pi ^2 x^2+56 x^2 \log (3)-16 x^2 \log ^2(3)}\right )-2 \log (x)+\log (x) \log \left (e^x x-x^3 (7 i+4 \pi -4 i \log (3))^2\right )-\log \left (e^{2 x}+98 e^x x^2-32 e^x \pi ^2 x^2+2401 x^4+1568 \pi ^2 x^4+256 \pi ^4 x^4-112 e^x x^2 \log (3)-5488 x^4 \log (3)-1792 \pi ^2 x^4 \log (3)+32 e^x x^2 \log ^2(3)+4704 x^4 \log ^2(3)+512 \pi ^2 x^4 \log ^2(3)-1792 x^4 \log ^3(3)+256 x^4 \log ^4(3)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(-2 - 2*x) - 294*x^2 + 336*x^2*(I*Pi + Log[3]) - 96*x^2*(I*Pi + Log[3])^2 + (147*x^2 + E^x*(1 +
x) - 168*x^2*(I*Pi + Log[3]) + 48*x^2*(I*Pi + Log[3])^2)*Log[x] + (E^x + 49*x^2 - 56*x^2*(I*Pi + Log[3]) + 16
*x^2*(I*Pi + Log[3])^2)*Log[E^x*x + 49*x^3 - 56*x^3*(I*Pi + Log[3]) + 16*x^3*(I*Pi + Log[3])^2])/(E^x*x + 49*x
^3 - 56*x^3*(I*Pi + Log[3]) + 16*x^3*(I*Pi + Log[3])^2),x]

[Out]

(2*I)*ArcTan[(8*Pi*x^2*(-7 + 4*Log[3]))/(-E^x - 49*x^2 + 16*Pi^2*x^2 + 56*x^2*Log[3] - 16*x^2*Log[3]^2)] - 2*L
og[x] + Log[x]*Log[E^x*x - x^3*(7*I + 4*Pi - (4*I)*Log[3])^2] - Log[E^(2*x) + 98*E^x*x^2 - 32*E^x*Pi^2*x^2 + 2
401*x^4 + 1568*Pi^2*x^4 + 256*Pi^4*x^4 - 112*E^x*x^2*Log[3] - 5488*x^4*Log[3] - 1792*Pi^2*x^4*Log[3] + 32*E^x*
x^2*Log[3]^2 + 4704*x^4*Log[3]^2 + 512*Pi^2*x^4*Log[3]^2 - 1792*x^4*Log[3]^3 + 256*x^4*Log[3]^4]

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fricas [A]  time = 0.75, size = 46, normalized size = 1.53 \begin {gather*} {\left (\log \relax (x) - 2\right )} \log \left (-8 \, {\left (-4 i \, \pi + 7\right )} x^{3} \log \relax (3) + 16 \, x^{3} \log \relax (3)^{2} + {\left (-56 i \, \pi - 16 \, \pi ^{2} + 49\right )} x^{3} + x e^{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+16*x^2*(log(3)+I*pi)^2-56*x^2*(log(3)+I*pi)+49*x^2)*log(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*
x^3*(log(3)+I*pi)+49*x^3)+((x+1)*exp(x)+48*x^2*(log(3)+I*pi)^2-168*x^2*(log(3)+I*pi)+147*x^2)*log(x)+(-2*x-2)*
exp(x)-96*x^2*(log(3)+I*pi)^2+336*x^2*(log(3)+I*pi)-294*x^2)/(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*x^3*(log(3)+I
*pi)+49*x^3),x, algorithm="fricas")

[Out]

(log(x) - 2)*log(-8*(-4*I*pi + 7)*x^3*log(3) + 16*x^3*log(3)^2 + (-56*I*pi - 16*pi^2 + 49)*x^3 + x*e^x)

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giac [B]  time = 0.46, size = 108, normalized size = 3.60 \begin {gather*} \log \left (-16 \, \pi ^{2} x^{2} + 32 i \, \pi x^{2} \log \relax (3) + 16 \, x^{2} \log \relax (3)^{2} - 56 i \, \pi x^{2} - 56 \, x^{2} \log \relax (3) + 49 \, x^{2} + e^{x}\right ) \log \relax (x) + \log \relax (x)^{2} - 2 \, \log \left (-16 \, \pi ^{2} x^{2} + 32 i \, \pi x^{2} \log \relax (3) + 16 \, x^{2} \log \relax (3)^{2} - 56 i \, \pi x^{2} - 56 \, x^{2} \log \relax (3) + 49 \, x^{2} + e^{x}\right ) - 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+16*x^2*(log(3)+I*pi)^2-56*x^2*(log(3)+I*pi)+49*x^2)*log(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*
x^3*(log(3)+I*pi)+49*x^3)+((x+1)*exp(x)+48*x^2*(log(3)+I*pi)^2-168*x^2*(log(3)+I*pi)+147*x^2)*log(x)+(-2*x-2)*
exp(x)-96*x^2*(log(3)+I*pi)^2+336*x^2*(log(3)+I*pi)-294*x^2)/(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*x^3*(log(3)+I
*pi)+49*x^3),x, algorithm="giac")

[Out]

log(-16*pi^2*x^2 + 32*I*pi*x^2*log(3) + 16*x^2*log(3)^2 - 56*I*pi*x^2 - 56*x^2*log(3) + 49*x^2 + e^x)*log(x) +
log(x)^2 - 2*log(-16*pi^2*x^2 + 32*I*pi*x^2*log(3) + 16*x^2*log(3)^2 - 56*I*pi*x^2 - 56*x^2*log(3) + 49*x^2 +
e^x) - 2*log(x)

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maple [C]  time = 0.77, size = 483, normalized size = 16.10

method	result	size
risch	\(\ln \relax (x ) \ln \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )+\ln \relax (x )^{2}-\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )}{2}+\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{2}}{2}+\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{2}}{2}-\frac {i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \left (-\pi ^{2} x^{2}+\left (2 i \ln \relax (3) x^{2}-\frac {7 i x^{2}}{2}\right ) \pi +x^{2} \ln \relax (3)^{2}-\frac {7 x^{2} \ln \relax (3)}{2}+\frac {49 x^{2}}{16}+\frac {{\mathrm e}^{x}}{16}\right )\right )^{3}}{2}-2 \ln \relax (x )-2 \ln \left (-16 \pi ^{2} x^{2}+32 i \pi \ln \relax (3) x^{2}-56 i \pi \,x^{2}+16 x^{2} \ln \relax (3)^{2}-56 x^{2} \ln \relax (3)+49 x^{2}+{\mathrm e}^{x}\right )\)	\(483\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp(x)+16*x^2*(ln(3)+I*Pi)^2-56*x^2*(ln(3)+I*Pi)+49*x^2)*ln(exp(x)*x+16*x^3*(ln(3)+I*Pi)^2-56*x^3*(ln(3)
+I*Pi)+49*x^3)+((x+1)*exp(x)+48*x^2*(ln(3)+I*Pi)^2-168*x^2*(ln(3)+I*Pi)+147*x^2)*ln(x)+(-2*x-2)*exp(x)-96*x^2*
(ln(3)+I*Pi)^2+336*x^2*(ln(3)+I*Pi)-294*x^2)/(exp(x)*x+16*x^3*(ln(3)+I*Pi)^2-56*x^3*(ln(3)+I*Pi)+49*x^3),x,met
hod=_RETURNVERBOSE)

[Out]

ln(x)*ln(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16*exp(x))+ln(x)^2-1/2*I
*Pi*ln(x)*csgn(I*x)*csgn(I*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16*ex
p(x)))*csgn(I*x*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16*exp(x)))+1/2*
I*Pi*ln(x)*csgn(I*x)*csgn(I*x*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16
*exp(x)))^2+1/2*I*Pi*ln(x)*csgn(I*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+
1/16*exp(x)))*csgn(I*x*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16*exp(x)
))^2-1/2*I*Pi*ln(x)*csgn(I*x*(-Pi^2*x^2+(2*I*ln(3)*x^2-7/2*I*x^2)*Pi+x^2*ln(3)^2-7/2*x^2*ln(3)+49/16*x^2+1/16*
exp(x)))^3-2*ln(x)-2*ln(-16*Pi^2*x^2+32*I*Pi*ln(3)*x^2-56*I*Pi*x^2+16*x^2*ln(3)^2-56*x^2*ln(3)+49*x^2+exp(x))

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maxima [A]  time = 0.51, size = 47, normalized size = 1.57 \begin {gather*} {\left (\log \relax (x) - 2\right )} \log \left ({\left (-56 i \, \pi - 16 \, \pi ^{2} - 8 \, {\left (-4 i \, \pi + 7\right )} \log \relax (3) + 16 \, \log \relax (3)^{2} + 49\right )} x^{2} + e^{x}\right ) + \log \relax (x)^{2} - 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+16*x^2*(log(3)+I*pi)^2-56*x^2*(log(3)+I*pi)+49*x^2)*log(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*
x^3*(log(3)+I*pi)+49*x^3)+((x+1)*exp(x)+48*x^2*(log(3)+I*pi)^2-168*x^2*(log(3)+I*pi)+147*x^2)*log(x)+(-2*x-2)*
exp(x)-96*x^2*(log(3)+I*pi)^2+336*x^2*(log(3)+I*pi)-294*x^2)/(exp(x)*x+16*x^3*(log(3)+I*pi)^2-56*x^3*(log(3)+I
*pi)+49*x^3),x, algorithm="maxima")

[Out]

(log(x) - 2)*log((-56*I*pi - 16*pi^2 - 8*(-4*I*pi + 7)*log(3) + 16*log(3)^2 + 49)*x^2 + e^x) + log(x)^2 - 2*lo
g(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {96\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-\ln \left (16\,x^3\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^3\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+x\,{\mathrm {e}}^x+49\,x^3\right )\,\left ({\mathrm {e}}^x+16\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+49\,x^2\right )+{\mathrm {e}}^x\,\left (2\,x+2\right )-336\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )-\ln \relax (x)\,\left (48\,x^2\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2+{\mathrm {e}}^x\,\left (x+1\right )-168\,x^2\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+147\,x^2\right )+294\,x^2}{16\,x^3\,{\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )}^2-56\,x^3\,\left (\ln \relax (3)+\Pi \,1{}\mathrm {i}\right )+x\,{\mathrm {e}}^x+49\,x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(96*x^2*(Pi*1i + log(3))^2 - log(16*x^3*(Pi*1i + log(3))^2 - 56*x^3*(Pi*1i + log(3)) + x*exp(x) + 49*x^3)
*(exp(x) + 16*x^2*(Pi*1i + log(3))^2 - 56*x^2*(Pi*1i + log(3)) + 49*x^2) + exp(x)*(2*x + 2) - 336*x^2*(Pi*1i +
log(3)) - log(x)*(48*x^2*(Pi*1i + log(3))^2 + exp(x)*(x + 1) - 168*x^2*(Pi*1i + log(3)) + 147*x^2) + 294*x^2)
/(16*x^3*(Pi*1i + log(3))^2 - 56*x^3*(Pi*1i + log(3)) + x*exp(x) + 49*x^3),x)

[Out]

int(-(96*x^2*(Pi*1i + log(3))^2 - log(16*x^3*(Pi*1i + log(3))^2 - 56*x^3*(Pi*1i + log(3)) + x*exp(x) + 49*x^3)
*(exp(x) + 16*x^2*(Pi*1i + log(3))^2 - 56*x^2*(Pi*1i + log(3)) + 49*x^2) + exp(x)*(2*x + 2) - 336*x^2*(Pi*1i +
log(3)) - log(x)*(48*x^2*(Pi*1i + log(3))^2 + exp(x)*(x + 1) - 168*x^2*(Pi*1i + log(3)) + 147*x^2) + 294*x^2)
/(16*x^3*(Pi*1i + log(3))^2 - 56*x^3*(Pi*1i + log(3)) + x*exp(x) + 49*x^3), x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+16*x**2*(ln(3)+I*pi)**2-56*x**2*(ln(3)+I*pi)+49*x**2)*ln(exp(x)*x+16*x**3*(ln(3)+I*pi)**2-5
6*x**3*(ln(3)+I*pi)+49*x**3)+((x+1)*exp(x)+48*x**2*(ln(3)+I*pi)**2-168*x**2*(ln(3)+I*pi)+147*x**2)*ln(x)+(-2*x
-2)*exp(x)-96*x**2*(ln(3)+I*pi)**2+336*x**2*(ln(3)+I*pi)-294*x**2)/(exp(x)*x+16*x**3*(ln(3)+I*pi)**2-56*x**3*(
ln(3)+I*pi)+49*x**3),x)

[Out]

Timed out

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