3.67.56 \(\int \frac {50 x^4+10 x^5-10 x^6+e^x (-50 x^2-10 x^3+10 x^4)+(100 x^3+10 x^4-20 x^5+e^x (-100 x-10 x^2+20 x^3)) \log (x)+(50 x^2-10 x^4+e^x (-50+10 x^2)) \log ^2(x)+(-51 x^4-9 x^5+8 x^6+e^x (x^2+24 x^3+7 x^4-5 x^5)+(-100 x^3-8 x^4+16 x^5+e^x (48 x^2+9 x^3-10 x^4)) \log (x)+(-50 x^2+8 x^4+e^x (25 x+2 x^2-5 x^3)) \log ^2(x)) \log (x^2)+(10 x^4+2 x^5-2 x^6+e^x (-10 x^2-2 x^3+2 x^4)+(20 x^3+2 x^4-4 x^5+e^x (-20 x-2 x^2+4 x^3)) \log (x)+(10 x^2-2 x^4+e^x (-10+2 x^2)) \log ^2(x)+(-10 x^4-2 x^5+2 x^6+e^x (5 x^3+x^4-x^5)+(-20 x^3-2 x^4+4 x^5+e^x (10 x^2+x^3-2 x^4)) \log (x)+(-10 x^2+2 x^4+e^x (5 x-x^3)) \log ^2(x)) \log (x^2)) \log (\frac {5 x+x^2-x^3+(5-x^2) \log (x)}{x+\log (x)})}{-5 x^7-x^8+x^9+e^{2 x} (-5 x^3-x^4+x^5)+e^x (10 x^5+2 x^6-2 x^7)+(-10 x^6-x^7+2 x^8+e^{2 x} (-10 x^2-x^3+2 x^4)+e^x (20 x^4+2 x^5-4 x^6)) \log (x)+(-5 x^5+x^7+e^{2 x} (-5 x+x^3)+e^x (10 x^3-2 x^5)) \log ^2(x)} \, dx\)

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

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(50*x^4 + 10*x^5 - 10*x^6 + E^x*(-50*x^2 - 10*x^3 + 10*x^4) + (100*x^3 + 10*x^4 - 20*x^5 + E^x*(-100*x - 1
0*x^2 + 20*x^3))*Log[x] + (50*x^2 - 10*x^4 + E^x*(-50 + 10*x^2))*Log[x]^2 + (-51*x^4 - 9*x^5 + 8*x^6 + E^x*(x^
2 + 24*x^3 + 7*x^4 - 5*x^5) + (-100*x^3 - 8*x^4 + 16*x^5 + E^x*(48*x^2 + 9*x^3 - 10*x^4))*Log[x] + (-50*x^2 +
8*x^4 + E^x*(25*x + 2*x^2 - 5*x^3))*Log[x]^2)*Log[x^2] + (10*x^4 + 2*x^5 - 2*x^6 + E^x*(-10*x^2 - 2*x^3 + 2*x^
4) + (20*x^3 + 2*x^4 - 4*x^5 + E^x*(-20*x - 2*x^2 + 4*x^3))*Log[x] + (10*x^2 - 2*x^4 + E^x*(-10 + 2*x^2))*Log[
x]^2 + (-10*x^4 - 2*x^5 + 2*x^6 + E^x*(5*x^3 + x^4 - x^5) + (-20*x^3 - 2*x^4 + 4*x^5 + E^x*(10*x^2 + x^3 - 2*x
^4))*Log[x] + (-10*x^2 + 2*x^4 + E^x*(5*x - x^3))*Log[x]^2)*Log[x^2])*Log[(5*x + x^2 - x^3 + (5 - x^2)*Log[x])
/(x + Log[x])])/(-5*x^7 - x^8 + x^9 + E^(2*x)*(-5*x^3 - x^4 + x^5) + E^x*(10*x^5 + 2*x^6 - 2*x^7) + (-10*x^6 -
x^7 + 2*x^8 + E^(2*x)*(-10*x^2 - x^3 + 2*x^4) + E^x*(20*x^4 + 2*x^5 - 4*x^6))*Log[x] + (-5*x^5 + x^7 + E^(2*x
)*(-5*x + x^3) + E^x*(10*x^3 - 2*x^5))*Log[x]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 1.80, size = 46, normalized size = 1.31 \begin {gather*} \frac {\log \left (x^2\right ) \left (5+\log \left (\frac {x \left (5+x-x^2\right )-\left (-5+x^2\right ) \log (x)}{x+\log (x)}\right )\right )}{e^x-x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(50*x^4 + 10*x^5 - 10*x^6 + E^x*(-50*x^2 - 10*x^3 + 10*x^4) + (100*x^3 + 10*x^4 - 20*x^5 + E^x*(-100
*x - 10*x^2 + 20*x^3))*Log[x] + (50*x^2 - 10*x^4 + E^x*(-50 + 10*x^2))*Log[x]^2 + (-51*x^4 - 9*x^5 + 8*x^6 + E
^x*(x^2 + 24*x^3 + 7*x^4 - 5*x^5) + (-100*x^3 - 8*x^4 + 16*x^5 + E^x*(48*x^2 + 9*x^3 - 10*x^4))*Log[x] + (-50*
x^2 + 8*x^4 + E^x*(25*x + 2*x^2 - 5*x^3))*Log[x]^2)*Log[x^2] + (10*x^4 + 2*x^5 - 2*x^6 + E^x*(-10*x^2 - 2*x^3
+ 2*x^4) + (20*x^3 + 2*x^4 - 4*x^5 + E^x*(-20*x - 2*x^2 + 4*x^3))*Log[x] + (10*x^2 - 2*x^4 + E^x*(-10 + 2*x^2)
)*Log[x]^2 + (-10*x^4 - 2*x^5 + 2*x^6 + E^x*(5*x^3 + x^4 - x^5) + (-20*x^3 - 2*x^4 + 4*x^5 + E^x*(10*x^2 + x^3
- 2*x^4))*Log[x] + (-10*x^2 + 2*x^4 + E^x*(5*x - x^3))*Log[x]^2)*Log[x^2])*Log[(5*x + x^2 - x^3 + (5 - x^2)*L
og[x])/(x + Log[x])])/(-5*x^7 - x^8 + x^9 + E^(2*x)*(-5*x^3 - x^4 + x^5) + E^x*(10*x^5 + 2*x^6 - 2*x^7) + (-10
*x^6 - x^7 + 2*x^8 + E^(2*x)*(-10*x^2 - x^3 + 2*x^4) + E^x*(20*x^4 + 2*x^5 - 4*x^6))*Log[x] + (-5*x^5 + x^7 +
E^(2*x)*(-5*x + x^3) + E^x*(10*x^3 - 2*x^5))*Log[x]^2),x]

[Out]

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

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fricas [A]  time = 0.51, size = 49, normalized size = 1.40 \begin {gather*} -\frac {2 \, {\left (\log \relax (x) \log \left (-\frac {x^{3} - x^{2} + {\left (x^{2} - 5\right )} \log \relax (x) - 5 \, x}{x + \log \relax (x)}\right ) + 5 \, \log \relax (x)\right )}}{x^{2} - e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+
(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-2
0*x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10*x^4)*log(((-x^2+5)*log(x)-x^
3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+25*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x
^5-8*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*log(x^2)+((10*x^2-50)*exp(x)-10*
x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)
-10*x^6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*log(x)^2+((2*x^4-x^3-10*x^2)*exp
(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp
(x)+x^9-x^8-5*x^7),x, algorithm="fricas")

[Out]

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

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giac [A]  time = 2.72, size = 53, normalized size = 1.51 \begin {gather*} -\frac {2 \, {\left (\log \left (-x^{3} - x^{2} \log \relax (x) + x^{2} + 5 \, x + 5 \, \log \relax (x)\right ) \log \relax (x) - \log \left (x + \log \relax (x)\right ) \log \relax (x) + 5 \, \log \relax (x)\right )}}{x^{2} - e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+
(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-2
0*x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10*x^4)*log(((-x^2+5)*log(x)-x^
3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+25*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x
^5-8*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*log(x^2)+((10*x^2-50)*exp(x)-10*
x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)
-10*x^6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*log(x)^2+((2*x^4-x^3-10*x^2)*exp
(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp
(x)+x^9-x^8-5*x^7),x, algorithm="giac")

[Out]

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

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maple [C]  time = 1.07, size = 1449, normalized size = 41.40

method	result	size
risch	\(-\frac {\left (-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 \ln \relax (x )\right ) \ln \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{2 \left (-{\mathrm e}^{x}+x^{2}\right )}+\frac {-40 \ln \relax (x )-4 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}+2 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-2 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3} \ln \left (x +\ln \relax (x )\right )-4 i \pi \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{3} \ln \relax (x )+10 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-20 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+8 i \pi \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2} \ln \relax (x )-\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{3}+2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{3}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}+8 \ln \relax (x ) \ln \left (x +\ln \relax (x )\right )+10 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-8 i \pi \ln \relax (x )-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{3}+2 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-2 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )-2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )+4 i \pi \,\mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right ) \ln \relax (x )+\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )+2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}+2 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-\pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2}-4 i \pi \,\mathrm {csgn}\left (\frac {i}{x +\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2} \ln \relax (x )-4 i \pi \,\mathrm {csgn}\left (i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{3}+\left (\ln \relax (x )-1\right ) x^{2}-5 x -5 \ln \relax (x )\right )}{x +\ln \relax (x )}\right )^{2} \ln \relax (x )+4 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \ln \left (x +\ln \relax (x )\right )-2 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \ln \left (x +\ln \relax (x )\right )-2 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}}{-4 \,{\mathrm e}^{x}+4 x^{2}}\)	\(1449\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*ln(x)^2+((-2*x^4+x^3+10*x^2)*exp(x)+4*x^5-2*x^4-20*x^3)*ln(x)+(-x^5+x^
4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)*ln(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*ln(x)^2+((4*x^3-2*x^2-20*x)*exp(x
)-4*x^5+2*x^4+20*x^3)*ln(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10*x^4)*ln(((-x^2+5)*ln(x)-x^3+x^2+5*x)/(x
+ln(x)))+(((-5*x^3+2*x^2+25*x)*exp(x)+8*x^4-50*x^2)*ln(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x^5-8*x^4-100*x^
3)*ln(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*ln(x^2)+((10*x^2-50)*exp(x)-10*x^4+50*x^2)*ln(x)
^2+((20*x^3-10*x^2-100*x)*exp(x)-20*x^5+10*x^4+100*x^3)*ln(x)+(10*x^4-10*x^3-50*x^2)*exp(x)-10*x^6+10*x^5+50*x
^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*ln(x)^2+((2*x^4-x^3-10*x^2)*exp(x)^2+(-4*x^6+2*x^5+
20*x^4)*exp(x)+2*x^8-x^7-10*x^6)*ln(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp(x)+x^9-x^8-5*x^7),x,
method=_RETURNVERBOSE)

[Out]

-1/2*(-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x^2)^3+4*ln(x))/(-exp(x)+x^2)*l
n(x^3+(ln(x)-1)*x^2-5*x-5*ln(x))+1/4*(-40*ln(x)+10*I*Pi*csgn(I*x)^2*csgn(I*x^2)-20*I*Pi*csgn(I*x)*csgn(I*x^2)^
2+8*I*Pi*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2*ln(x)-Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/(x+ln(x
))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^3+2*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5
*ln(x)))^3-Pi^2*csgn(I*x^2)^3*csgn(I/(x+ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-Pi^2*csgn(
I*x^2)^3*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-4*Pi^2*cs
gn(I*x)*csgn(I*x^2)^2*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2+2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(
I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-2*I*Pi*csgn(I*x^2)^3*ln(x+ln(x))-8*I*Pi*ln(x)+8*ln(x)*ln(x+ln(x
))+Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/(x+ln(x))*(x^
3+(ln(x)-1)*x^2-5*x-5*ln(x)))-2*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5
*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))+4*I*Pi*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-
5*x-5*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*ln(x)-Pi^2*csgn(I*x^2)^3*csgn(I/(x+ln(x))*(x^3
+(ln(x)-1)*x^2-5*x-5*ln(x)))^3+Pi^2*csgn(I*x^2)^3*csgn(I/(x+ln(x)))*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*cs
gn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))+2*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5
*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/(x+ln(x)))*cs
gn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2+2*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/(x+ln(x)))*csgn(I/(x+l
n(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))*
csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-4*I*Pi*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^3
*ln(x)-4*I*Pi*csgn(I/(x+ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2*ln(x)-4*I*Pi*csgn(I*(x^3+(
ln(x)-1)*x^2-5*x-5*ln(x)))*csgn(I/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2*ln(x)+4*I*Pi*csgn(I*x)*csgn(I*x
^2)^2*ln(x+ln(x))-2*I*Pi*csgn(I*x)^2*csgn(I*x^2)*ln(x+ln(x))+10*I*Pi*csgn(I*x^2)^3+2*Pi^2*csgn(I*x^2)^3*csgn(I
/(x+ln(x))*(x^3+(ln(x)-1)*x^2-5*x-5*ln(x)))^2-2*Pi^2*csgn(I*x)^2*csgn(I*x^2)+4*Pi^2*csgn(I*x)*csgn(I*x^2)^2-2*
Pi^2*csgn(I*x^2)^3)/(-exp(x)+x^2)

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maxima [A]  time = 0.71, size = 51, normalized size = 1.46 \begin {gather*} -\frac {2 \, {\left (\log \left (-x^{3} + x^{2} - {\left (x^{2} - 5\right )} \log \relax (x) + 5 \, x\right ) \log \relax (x) - \log \left (x + \log \relax (x)\right ) \log \relax (x) + 5 \, \log \relax (x)\right )}}{x^{2} - e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((((-x^3+5*x)*exp(x)+2*x^4-10*x^2)*log(x)^2+((-2*x^4+x^3+10*x^2)*exp(x)+4*x^5-2*x^4-20*x^3)*log(x)+
(-x^5+x^4+5*x^3)*exp(x)+2*x^6-2*x^5-10*x^4)*log(x^2)+((2*x^2-10)*exp(x)-2*x^4+10*x^2)*log(x)^2+((4*x^3-2*x^2-2
0*x)*exp(x)-4*x^5+2*x^4+20*x^3)*log(x)+(2*x^4-2*x^3-10*x^2)*exp(x)-2*x^6+2*x^5+10*x^4)*log(((-x^2+5)*log(x)-x^
3+x^2+5*x)/(x+log(x)))+(((-5*x^3+2*x^2+25*x)*exp(x)+8*x^4-50*x^2)*log(x)^2+((-10*x^4+9*x^3+48*x^2)*exp(x)+16*x
^5-8*x^4-100*x^3)*log(x)+(-5*x^5+7*x^4+24*x^3+x^2)*exp(x)+8*x^6-9*x^5-51*x^4)*log(x^2)+((10*x^2-50)*exp(x)-10*
x^4+50*x^2)*log(x)^2+((20*x^3-10*x^2-100*x)*exp(x)-20*x^5+10*x^4+100*x^3)*log(x)+(10*x^4-10*x^3-50*x^2)*exp(x)
-10*x^6+10*x^5+50*x^4)/(((x^3-5*x)*exp(x)^2+(-2*x^5+10*x^3)*exp(x)+x^7-5*x^5)*log(x)^2+((2*x^4-x^3-10*x^2)*exp
(x)^2+(-4*x^6+2*x^5+20*x^4)*exp(x)+2*x^8-x^7-10*x^6)*log(x)+(x^5-x^4-5*x^3)*exp(x)^2+(-2*x^7+2*x^6+10*x^5)*exp
(x)+x^9-x^8-5*x^7),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 5.23, size = 48, normalized size = 1.37 \begin {gather*} \frac {\ln \left (x^2\right )\,\left (\ln \left (\frac {5\,x+5\,\ln \relax (x)-x^2\,\ln \relax (x)+x^2-x^3}{x+\ln \relax (x)}\right )+5\right )}{{\mathrm {e}}^x-x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(100*x^3 + 10*x^4 - 20*x^5 - exp(x)*(100*x + 10*x^2 - 20*x^3)) - exp(x)*(50*x^2 + 10*x^3 - 10*x^4
) + log(x)^2*(exp(x)*(10*x^2 - 50) + 50*x^2 - 10*x^4) + log((5*x - log(x)*(x^2 - 5) + x^2 - x^3)/(x + log(x)))
*(log(x)*(20*x^3 + 2*x^4 - 4*x^5 - exp(x)*(20*x + 2*x^2 - 4*x^3)) - exp(x)*(10*x^2 + 2*x^3 - 2*x^4) + log(x)^2
*(exp(x)*(2*x^2 - 10) + 10*x^2 - 2*x^4) + log(x^2)*(log(x)^2*(exp(x)*(5*x - x^3) - 10*x^2 + 2*x^4) - log(x)*(2
0*x^3 + 2*x^4 - 4*x^5 - exp(x)*(10*x^2 + x^3 - 2*x^4)) - 10*x^4 - 2*x^5 + 2*x^6 + exp(x)*(5*x^3 + x^4 - x^5))
+ 10*x^4 + 2*x^5 - 2*x^6) + log(x^2)*(exp(x)*(x^2 + 24*x^3 + 7*x^4 - 5*x^5) + log(x)^2*(8*x^4 - 50*x^2 + exp(x
)*(25*x + 2*x^2 - 5*x^3)) + log(x)*(exp(x)*(48*x^2 + 9*x^3 - 10*x^4) - 100*x^3 - 8*x^4 + 16*x^5) - 51*x^4 - 9*
x^5 + 8*x^6) + 50*x^4 + 10*x^5 - 10*x^6)/(exp(2*x)*(5*x^3 + x^4 - x^5) - exp(x)*(10*x^5 + 2*x^6 - 2*x^7) + log
(x)*(exp(2*x)*(10*x^2 + x^3 - 2*x^4) - exp(x)*(20*x^4 + 2*x^5 - 4*x^6) + 10*x^6 + x^7 - 2*x^8) + log(x)^2*(exp
(2*x)*(5*x - x^3) - exp(x)*(10*x^3 - 2*x^5) + 5*x^5 - x^7) + 5*x^7 + x^8 - x^9),x)

[Out]

(log(x^2)*(log((5*x + 5*log(x) - x^2*log(x) + x^2 - x^3)/(x + log(x))) + 5))/(exp(x) - x^2)

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sympy [A]  time = 1.57, size = 41, normalized size = 1.17 \begin {gather*} \frac {2 \log {\relax (x )} \log {\left (\frac {- x^{3} + x^{2} + 5 x + \left (5 - x^{2}\right ) \log {\relax (x )}}{x + \log {\relax (x )}} \right )} + 10 \log {\relax (x )}}{- x^{2} + e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((((-x**3+5*x)*exp(x)+2*x**4-10*x**2)*ln(x)**2+((-2*x**4+x**3+10*x**2)*exp(x)+4*x**5-2*x**4-20*x**3
)*ln(x)+(-x**5+x**4+5*x**3)*exp(x)+2*x**6-2*x**5-10*x**4)*ln(x**2)+((2*x**2-10)*exp(x)-2*x**4+10*x**2)*ln(x)**
2+((4*x**3-2*x**2-20*x)*exp(x)-4*x**5+2*x**4+20*x**3)*ln(x)+(2*x**4-2*x**3-10*x**2)*exp(x)-2*x**6+2*x**5+10*x*
*4)*ln(((-x**2+5)*ln(x)-x**3+x**2+5*x)/(x+ln(x)))+(((-5*x**3+2*x**2+25*x)*exp(x)+8*x**4-50*x**2)*ln(x)**2+((-1
0*x**4+9*x**3+48*x**2)*exp(x)+16*x**5-8*x**4-100*x**3)*ln(x)+(-5*x**5+7*x**4+24*x**3+x**2)*exp(x)+8*x**6-9*x**
5-51*x**4)*ln(x**2)+((10*x**2-50)*exp(x)-10*x**4+50*x**2)*ln(x)**2+((20*x**3-10*x**2-100*x)*exp(x)-20*x**5+10*
x**4+100*x**3)*ln(x)+(10*x**4-10*x**3-50*x**2)*exp(x)-10*x**6+10*x**5+50*x**4)/(((x**3-5*x)*exp(x)**2+(-2*x**5
+10*x**3)*exp(x)+x**7-5*x**5)*ln(x)**2+((2*x**4-x**3-10*x**2)*exp(x)**2+(-4*x**6+2*x**5+20*x**4)*exp(x)+2*x**8
-x**7-10*x**6)*ln(x)+(x**5-x**4-5*x**3)*exp(x)**2+(-2*x**7+2*x**6+10*x**5)*exp(x)+x**9-x**8-5*x**7),x)

[Out]

(2*log(x)*log((-x**3 + x**2 + 5*x + (5 - x**2)*log(x))/(x + log(x))) + 10*log(x))/(-x**2 + exp(x))

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