3.37.10 \(\int \frac {1000+1000 x+e^{x^2} (80 x-20 x^2-200 x^3-200 x^4)+e^{2 x^2} (-2 x^2-20 x^4)+(-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} (-36 x-96 x^2+80 x^3+80 x^4)) \log (x)+(120+1220 x+600 x^2+e^{x^2} (4 x+30 x^2-8 x^3-108 x^4)) \log ^2(x)+(-8-428 x-620 x^2+e^{x^2} (-2 x^2+40 x^4)) \log ^3(x)+(68 x+308 x^2-4 e^{x^2} x^4) \log ^4(x)+(-4 x-60 x^2) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx\)

Optimal. Leaf size=29 \[ \left (1+\frac {2+x}{x}+\frac {e^{x^2}}{5-\log (x)}+\log ^2(x)\right )^2 \]

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Rubi [F]  time = 6.72, 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 {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1000 + 1000*x + E^x^2*(80*x - 20*x^2 - 200*x^3 - 200*x^4) + E^(2*x^2)*(-2*x^2 - 20*x^4) + (-600 - 1600*x
- 1000*x^2 + 4*E^(2*x^2)*x^4 + E^x^2*(-36*x - 96*x^2 + 80*x^3 + 80*x^4))*Log[x] + (120 + 1220*x + 600*x^2 + E^
x^2*(4*x + 30*x^2 - 8*x^3 - 108*x^4))*Log[x]^2 + (-8 - 428*x - 620*x^2 + E^x^2*(-2*x^2 + 40*x^4))*Log[x]^3 + (
68*x + 308*x^2 - 4*E^x^2*x^4)*Log[x]^4 + (-4*x - 60*x^2)*Log[x]^5 + 4*x^2*Log[x]^6)/(-125*x^3 + 75*x^3*Log[x]
- 15*x^3*Log[x]^2 + x^3*Log[x]^3),x]

[Out]

1200/x^2 + 1468/x + (3350*ExpIntegralEi[5 - Log[x]])/E^5 + (2600*ExpIntegralEi[2*(5 - Log[x])])/E^10 + (600*Ex
pIntegralEi[2*(5 - Log[x])]*(11 - 2*Log[x]))/E^10 - 2500/(5 - Log[x])^2 - 500/(x^2*(5 - Log[x])^2) + 5750/(x*(
5 - Log[x])^2) + 1000/(5 - Log[x]) - 1000/(x^2*(5 - Log[x])) - 7550/(x*(5 - Log[x])) - (300*(11 - 2*Log[x]))/(
x^2*(5 - Log[x])) - (800*ExpIntegralEi[5 - Log[x]]*(5 - Log[x]))/E^5 - (2400*ExpIntegralEi[2*(5 - Log[x])]*(5
- Log[x]))/E^10 + (8*Log[x])/x - (800*ExpIntegralEi[5 - Log[x]]*Log[x])/E^5 - (1200*ExpIntegralEi[2*(5 - Log[x
])]*Log[x])/E^10 + 60*(x^(-1) - 15*Log[x])*Log[x] + (300*Log[x])/(x^2*(5 - Log[x])^2) + (800*Log[x])/(x*(5 - L
og[x])^2) + (600*Log[x])/(x^2*(5 - Log[x])) + (800*Log[x])/(x*(5 - Log[x])) + 904*Log[x]^2 + (4*Log[x]^2)/x +
(100*Log[x]^2)/(5 - Log[x])^2 + Log[x]^4 + (E^(2*x^2)*(5*x^2 - x^2*Log[x]))/(x^2*(5 - Log[x])^3) + (2*E^x^2*(1
0*x^2 + 10*x^3 - 2*x^2*Log[x] - 2*x^3*Log[x] + 5*x^3*Log[x]^2 - x^3*Log[x]^3))/(x^3*(5 - Log[x])^2) + 120*Defe
r[Int][Log[x]^2/(x^3*(-5 + Log[x])^3), x] + 1220*Defer[Int][Log[x]^2/(x^2*(-5 + Log[x])^3), x] - 8*Defer[Int][
Log[x]^3/(x^3*(-5 + Log[x])^3), x] - 428*Defer[Int][Log[x]^3/(x^2*(-5 + Log[x])^3), x] + 68*Defer[Int][Log[x]^
4/(x^2*(-5 + Log[x])^3), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1000-1000 x-e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )-e^{2 x^2} \left (-2 x^2-20 x^4\right )-\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)-\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)-\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)-\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)-\left (-4 x-60 x^2\right ) \log ^5(x)-4 x^2 \log ^6(x)}{x^3 (5-\log (x))^3} \, dx\\ &=\int \left (\frac {1000}{x^3 (-5+\log (x))^3}+\frac {1000}{x^2 (-5+\log (x))^3}-\frac {600 \log (x)}{x^3 (-5+\log (x))^3}-\frac {1600 \log (x)}{x^2 (-5+\log (x))^3}-\frac {1000 \log (x)}{x (-5+\log (x))^3}+\frac {120 \log ^2(x)}{x^3 (-5+\log (x))^3}+\frac {1220 \log ^2(x)}{x^2 (-5+\log (x))^3}+\frac {600 \log ^2(x)}{x (-5+\log (x))^3}-\frac {8 \log ^3(x)}{x^3 (-5+\log (x))^3}-\frac {428 \log ^3(x)}{x^2 (-5+\log (x))^3}-\frac {620 \log ^3(x)}{x (-5+\log (x))^3}+\frac {68 \log ^4(x)}{x^2 (-5+\log (x))^3}+\frac {308 \log ^4(x)}{x (-5+\log (x))^3}-\frac {4 (1+15 x) \log ^5(x)}{x^2 (-5+\log (x))^3}+\frac {4 \log ^6(x)}{x (-5+\log (x))^3}+\frac {2 e^{2 x^2} \left (-1-10 x^2+2 x^2 \log (x)\right )}{x (-5+\log (x))^3}-\frac {2 e^{x^2} \left (8-2 x-20 x^2-20 x^3-2 \log (x)-10 x \log (x)+4 x^2 \log (x)+4 x^3 \log (x)+x \log ^2(x)-10 x^3 \log ^2(x)+2 x^3 \log ^3(x)\right )}{x^2 (-5+\log (x))^2}\right ) \, dx\\ &=2 \int \frac {e^{2 x^2} \left (-1-10 x^2+2 x^2 \log (x)\right )}{x (-5+\log (x))^3} \, dx-2 \int \frac {e^{x^2} \left (8-2 x-20 x^2-20 x^3-2 \log (x)-10 x \log (x)+4 x^2 \log (x)+4 x^3 \log (x)+x \log ^2(x)-10 x^3 \log ^2(x)+2 x^3 \log ^3(x)\right )}{x^2 (-5+\log (x))^2} \, dx-4 \int \frac {(1+15 x) \log ^5(x)}{x^2 (-5+\log (x))^3} \, dx+4 \int \frac {\log ^6(x)}{x (-5+\log (x))^3} \, dx-8 \int \frac {\log ^3(x)}{x^3 (-5+\log (x))^3} \, dx+68 \int \frac {\log ^4(x)}{x^2 (-5+\log (x))^3} \, dx+120 \int \frac {\log ^2(x)}{x^3 (-5+\log (x))^3} \, dx+308 \int \frac {\log ^4(x)}{x (-5+\log (x))^3} \, dx-428 \int \frac {\log ^3(x)}{x^2 (-5+\log (x))^3} \, dx-600 \int \frac {\log (x)}{x^3 (-5+\log (x))^3} \, dx+600 \int \frac {\log ^2(x)}{x (-5+\log (x))^3} \, dx-620 \int \frac {\log ^3(x)}{x (-5+\log (x))^3} \, dx+1000 \int \frac {1}{x^3 (-5+\log (x))^3} \, dx+1000 \int \frac {1}{x^2 (-5+\log (x))^3} \, dx-1000 \int \frac {\log (x)}{x (-5+\log (x))^3} \, dx+1220 \int \frac {\log ^2(x)}{x^2 (-5+\log (x))^3} \, dx-1600 \int \frac {\log (x)}{x^2 (-5+\log (x))^3} \, dx\\ &=-\frac {500}{x^2 (5-\log (x))^2}-\frac {500}{x (5-\log (x))^2}-\frac {800 \text {Ei}(5-\log (x)) \log (x)}{e^5}-\frac {1200 \text {Ei}(2 (5-\log (x))) \log (x)}{e^{10}}+\frac {300 \log (x)}{x^2 (5-\log (x))^2}+\frac {800 \log (x)}{x (5-\log (x))^2}+\frac {600 \log (x)}{x^2 (5-\log (x))}+\frac {800 \log (x)}{x (5-\log (x))}+\frac {e^{2 x^2} \left (5 x^2-x^2 \log (x)\right )}{x^2 (5-\log (x))^3}+\frac {2 e^{x^2} \left (10 x^2+10 x^3-2 x^2 \log (x)-2 x^3 \log (x)+5 x^3 \log ^2(x)-x^3 \log ^3(x)\right )}{x^3 (5-\log (x))^2}-4 \int \left (\frac {150 (1+15 x)}{x^2}+\frac {3125 (1+15 x)}{x^2 (-5+\log (x))^3}+\frac {3125 (1+15 x)}{x^2 (-5+\log (x))^2}+\frac {1250 (1+15 x)}{x^2 (-5+\log (x))}+\frac {15 (1+15 x) \log (x)}{x^2}+\frac {(1+15 x) \log ^2(x)}{x^2}\right ) \, dx+4 \operatorname {Subst}\left (\int \frac {x^6}{(-5+x)^3} \, dx,x,\log (x)\right )-8 \int \frac {\log ^3(x)}{x^3 (-5+\log (x))^3} \, dx+68 \int \frac {\log ^4(x)}{x^2 (-5+\log (x))^3} \, dx+120 \int \frac {\log ^2(x)}{x^3 (-5+\log (x))^3} \, dx+308 \operatorname {Subst}\left (\int \frac {x^4}{(-5+x)^3} \, dx,x,\log (x)\right )-428 \int \frac {\log ^3(x)}{x^2 (-5+\log (x))^3} \, dx-500 \int \frac {1}{x^2 (-5+\log (x))^2} \, dx+600 \int \left (\frac {2 \text {Ei}(-2 (-5+\log (x)))}{e^{10} x}+\frac {-11+2 \log (x)}{2 x^3 (-5+\log (x))^2}\right ) \, dx+600 \operatorname {Subst}\left (\int \frac {x^2}{(-5+x)^3} \, dx,x,\log (x)\right )-620 \operatorname {Subst}\left (\int \frac {x^3}{(-5+x)^3} \, dx,x,\log (x)\right )-1000 \int \frac {1}{x^3 (-5+\log (x))^2} \, dx-1000 \operatorname {Subst}\left (\int \frac {x}{(-5+x)^3} \, dx,x,\log (x)\right )+1220 \int \frac {\log ^2(x)}{x^2 (-5+\log (x))^3} \, dx+1600 \int \frac {\frac {x \text {Ei}(5-\log (x))}{e^5}+\frac {-6+\log (x)}{(-5+\log (x))^2}}{2 x^2} \, dx\\ &=-\frac {500}{x^2 (5-\log (x))^2}-\frac {500}{x (5-\log (x))^2}-\frac {1000}{x^2 (5-\log (x))}-\frac {500}{x (5-\log (x))}-\frac {800 \text {Ei}(5-\log (x)) \log (x)}{e^5}-\frac {1200 \text {Ei}(2 (5-\log (x))) \log (x)}{e^{10}}+\frac {300 \log (x)}{x^2 (5-\log (x))^2}+\frac {800 \log (x)}{x (5-\log (x))^2}+\frac {600 \log (x)}{x^2 (5-\log (x))}+\frac {800 \log (x)}{x (5-\log (x))}+\frac {100 \log ^2(x)}{(5-\log (x))^2}+\frac {e^{2 x^2} \left (5 x^2-x^2 \log (x)\right )}{x^2 (5-\log (x))^3}+\frac {2 e^{x^2} \left (10 x^2+10 x^3-2 x^2 \log (x)-2 x^3 \log (x)+5 x^3 \log ^2(x)-x^3 \log ^3(x)\right )}{x^3 (5-\log (x))^2}-4 \int \frac {(1+15 x) \log ^2(x)}{x^2} \, dx+4 \operatorname {Subst}\left (\int \left (1250+\frac {15625}{(-5+x)^3}+\frac {18750}{(-5+x)^2}+\frac {9375}{-5+x}+150 x+15 x^2+x^3\right ) \, dx,x,\log (x)\right )-8 \int \frac {\log ^3(x)}{x^3 (-5+\log (x))^3} \, dx-60 \int \frac {(1+15 x) \log (x)}{x^2} \, dx+68 \int \frac {\log ^4(x)}{x^2 (-5+\log (x))^3} \, dx+120 \int \frac {\log ^2(x)}{x^3 (-5+\log (x))^3} \, dx+300 \int \frac {-11+2 \log (x)}{x^3 (-5+\log (x))^2} \, dx+308 \operatorname {Subst}\left (\int \left (15+\frac {625}{(-5+x)^3}+\frac {500}{(-5+x)^2}+\frac {150}{-5+x}+x\right ) \, dx,x,\log (x)\right )-428 \int \frac {\log ^3(x)}{x^2 (-5+\log (x))^3} \, dx+500 \int \frac {1}{x^2 (-5+\log (x))} \, dx-600 \int \frac {1+15 x}{x^2} \, dx+600 \operatorname {Subst}\left (\int \left (\frac {25}{(-5+x)^3}+\frac {10}{(-5+x)^2}+\frac {1}{-5+x}\right ) \, dx,x,\log (x)\right )-620 \operatorname {Subst}\left (\int \left (1+\frac {125}{(-5+x)^3}+\frac {75}{(-5+x)^2}+\frac {15}{-5+x}\right ) \, dx,x,\log (x)\right )+800 \int \frac {\frac {x \text {Ei}(5-\log (x))}{e^5}+\frac {-6+\log (x)}{(-5+\log (x))^2}}{x^2} \, dx+1220 \int \frac {\log ^2(x)}{x^2 (-5+\log (x))^3} \, dx+2000 \int \frac {1}{x^3 (-5+\log (x))} \, dx-5000 \int \frac {1+15 x}{x^2 (-5+\log (x))} \, dx-12500 \int \frac {1+15 x}{x^2 (-5+\log (x))^3} \, dx-12500 \int \frac {1+15 x}{x^2 (-5+\log (x))^2} \, dx+\frac {1200 \int \frac {\text {Ei}(-2 (-5+\log (x)))}{x} \, dx}{e^{10}}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.30, size = 85, normalized size = 2.93 \begin {gather*} -2 \left (5 e^{x^2}-\frac {2}{x^2}-\frac {4}{x}-\frac {e^{2 x^2}}{2 (-5+\log (x))^2}+\frac {e^{x^2} (2+27 x)}{x (-5+\log (x))}+e^{x^2} \log (x)-\frac {2 (1+x) \log ^2(x)}{x}-\frac {\log ^4(x)}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1000 + 1000*x + E^x^2*(80*x - 20*x^2 - 200*x^3 - 200*x^4) + E^(2*x^2)*(-2*x^2 - 20*x^4) + (-600 - 1
600*x - 1000*x^2 + 4*E^(2*x^2)*x^4 + E^x^2*(-36*x - 96*x^2 + 80*x^3 + 80*x^4))*Log[x] + (120 + 1220*x + 600*x^
2 + E^x^2*(4*x + 30*x^2 - 8*x^3 - 108*x^4))*Log[x]^2 + (-8 - 428*x - 620*x^2 + E^x^2*(-2*x^2 + 40*x^4))*Log[x]
^3 + (68*x + 308*x^2 - 4*E^x^2*x^4)*Log[x]^4 + (-4*x - 60*x^2)*Log[x]^5 + 4*x^2*Log[x]^6)/(-125*x^3 + 75*x^3*L
og[x] - 15*x^3*Log[x]^2 + x^3*Log[x]^3),x]

[Out]

-2*(5*E^x^2 - 2/x^2 - 4/x - E^(2*x^2)/(2*(-5 + Log[x])^2) + (E^x^2*(2 + 27*x))/(x*(-5 + Log[x])) + E^x^2*Log[x
] - (2*(1 + x)*Log[x]^2)/x - Log[x]^4/2)

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fricas [B]  time = 0.48, size = 148, normalized size = 5.10 \begin {gather*} \frac {x^{2} \log \relax (x)^{6} - 10 \, x^{2} \log \relax (x)^{5} + {\left (29 \, x^{2} + 4 \, x\right )} \log \relax (x)^{4} - 2 \, {\left (x^{2} e^{\left (x^{2}\right )} + 20 \, x^{2} + 20 \, x\right )} \log \relax (x)^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (5 \, x^{2} e^{\left (x^{2}\right )} + 50 \, x^{2} + 54 \, x + 2\right )} \log \relax (x)^{2} + 20 \, {\left (x^{2} + x\right )} e^{\left (x^{2}\right )} - 4 \, {\left ({\left (x^{2} + x\right )} e^{\left (x^{2}\right )} + 20 \, x + 10\right )} \log \relax (x) + 200 \, x + 100}{x^{2} \log \relax (x)^{2} - 10 \, x^{2} \log \relax (x) + 25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x
^2)-620*x^2-428*x-8)*log(x)^3+((-108*x^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^
2)^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x^4-2*x^2)*exp(x^2)^2+(-200*x^4-200
*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/(x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm="fri
cas")

[Out]

(x^2*log(x)^6 - 10*x^2*log(x)^5 + (29*x^2 + 4*x)*log(x)^4 - 2*(x^2*e^(x^2) + 20*x^2 + 20*x)*log(x)^3 + x^2*e^(
2*x^2) + 2*(5*x^2*e^(x^2) + 50*x^2 + 54*x + 2)*log(x)^2 + 20*(x^2 + x)*e^(x^2) - 4*((x^2 + x)*e^(x^2) + 20*x +
10)*log(x) + 200*x + 100)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2)

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giac [B]  time = 0.25, size = 181, normalized size = 6.24 \begin {gather*} \frac {x^{2} \log \relax (x)^{6} - 10 \, x^{2} \log \relax (x)^{5} - 2 \, x^{2} e^{\left (x^{2}\right )} \log \relax (x)^{3} + 29 \, x^{2} \log \relax (x)^{4} + 10 \, x^{2} e^{\left (x^{2}\right )} \log \relax (x)^{2} - 40 \, x^{2} \log \relax (x)^{3} + 4 \, x \log \relax (x)^{4} - 4 \, x^{2} e^{\left (x^{2}\right )} \log \relax (x) + 100 \, x^{2} \log \relax (x)^{2} - 40 \, x \log \relax (x)^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 20 \, x^{2} e^{\left (x^{2}\right )} - 4 \, x e^{\left (x^{2}\right )} \log \relax (x) + 108 \, x \log \relax (x)^{2} + 20 \, x e^{\left (x^{2}\right )} - 80 \, x \log \relax (x) + 4 \, \log \relax (x)^{2} + 200 \, x - 40 \, \log \relax (x) + 100}{x^{2} \log \relax (x)^{2} - 10 \, x^{2} \log \relax (x) + 25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x
^2)-620*x^2-428*x-8)*log(x)^3+((-108*x^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^
2)^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x^4-2*x^2)*exp(x^2)^2+(-200*x^4-200
*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/(x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm="gia
c")

[Out]

(x^2*log(x)^6 - 10*x^2*log(x)^5 - 2*x^2*e^(x^2)*log(x)^3 + 29*x^2*log(x)^4 + 10*x^2*e^(x^2)*log(x)^2 - 40*x^2*
log(x)^3 + 4*x*log(x)^4 - 4*x^2*e^(x^2)*log(x) + 100*x^2*log(x)^2 - 40*x*log(x)^3 + x^2*e^(2*x^2) + 20*x^2*e^(
x^2) - 4*x*e^(x^2)*log(x) + 108*x*log(x)^2 + 20*x*e^(x^2) - 80*x*log(x) + 4*log(x)^2 + 200*x - 40*log(x) + 100
)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2)

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maple [B]  time = 0.07, size = 79, normalized size = 2.72

method	result	size
risch	\(\ln \relax (x )^{4}+\frac {4 \left (x +1\right ) \ln \relax (x )^{2}}{x}-2 \,{\mathrm e}^{x^{2}} \ln \relax (x )-\frac {2 \left (5 x^{2} {\mathrm e}^{x^{2}}-4 x -2\right )}{x^{2}}+\frac {{\mathrm e}^{x^{2}} \left ({\mathrm e}^{x^{2}} x -54 x \ln \relax (x )+270 x -4 \ln \relax (x )+20\right )}{\left (\ln \relax (x )-5\right )^{2} x}\)	\(79\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^2*ln(x)^6+(-60*x^2-4*x)*ln(x)^5+(-4*x^4*exp(x^2)+308*x^2+68*x)*ln(x)^4+((40*x^4-2*x^2)*exp(x^2)-620*x
^2-428*x-8)*ln(x)^3+((-108*x^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*ln(x)^2+(4*x^4*exp(x^2)^2+(80*x^
4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*ln(x)+(-20*x^4-2*x^2)*exp(x^2)^2+(-200*x^4-200*x^3-20*x^2+
80*x)*exp(x^2)+1000*x+1000)/(x^3*ln(x)^3-15*x^3*ln(x)^2+75*x^3*ln(x)-125*x^3),x,method=_RETURNVERBOSE)

[Out]

ln(x)^4+4*(x+1)/x*ln(x)^2-2*exp(x^2)*ln(x)-2*(5*x^2*exp(x^2)-4*x-2)/x^2+exp(x^2)*(exp(x^2)*x-54*x*ln(x)+270*x-
4*ln(x)+20)/(ln(x)-5)^2/x

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maxima [B]  time = 0.47, size = 147, normalized size = 5.07 \begin {gather*} \frac {x^{2} \log \relax (x)^{6} - 10 \, x^{2} \log \relax (x)^{5} + {\left (29 \, x^{2} + 4 \, x\right )} \log \relax (x)^{4} - 40 \, {\left (x^{2} + x\right )} \log \relax (x)^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 4 \, {\left (25 \, x^{2} + 27 \, x + 1\right )} \log \relax (x)^{2} - 2 \, {\left (x^{2} \log \relax (x)^{3} - 5 \, x^{2} \log \relax (x)^{2} - 10 \, x^{2} + 2 \, {\left (x^{2} + x\right )} \log \relax (x) - 10 \, x\right )} e^{\left (x^{2}\right )} - 40 \, {\left (2 \, x + 1\right )} \log \relax (x) + 200 \, x + 100}{x^{2} \log \relax (x)^{2} - 10 \, x^{2} \log \relax (x) + 25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x
^2)-620*x^2-428*x-8)*log(x)^3+((-108*x^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^
2)^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x^4-2*x^2)*exp(x^2)^2+(-200*x^4-200
*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/(x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm="max
ima")

[Out]

(x^2*log(x)^6 - 10*x^2*log(x)^5 + (29*x^2 + 4*x)*log(x)^4 - 40*(x^2 + x)*log(x)^3 + x^2*e^(2*x^2) + 4*(25*x^2
+ 27*x + 1)*log(x)^2 - 2*(x^2*log(x)^3 - 5*x^2*log(x)^2 - 10*x^2 + 2*(x^2 + x)*log(x) - 10*x)*e^(x^2) - 40*(2*
x + 1)*log(x) + 200*x + 100)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int -\frac {1000\,x-{\ln \relax (x)}^5\,\left (60\,x^2+4\,x\right )-{\mathrm {e}}^{x^2}\,\left (200\,x^4+200\,x^3+20\,x^2-80\,x\right )-{\ln \relax (x)}^3\,\left (428\,x+{\mathrm {e}}^{x^2}\,\left (2\,x^2-40\,x^4\right )+620\,x^2+8\right )+4\,x^2\,{\ln \relax (x)}^6+{\ln \relax (x)}^4\,\left (68\,x-4\,x^4\,{\mathrm {e}}^{x^2}+308\,x^2\right )+{\ln \relax (x)}^2\,\left (1220\,x+{\mathrm {e}}^{x^2}\,\left (-108\,x^4-8\,x^3+30\,x^2+4\,x\right )+600\,x^2+120\right )-{\mathrm {e}}^{2\,x^2}\,\left (20\,x^4+2\,x^2\right )-\ln \relax (x)\,\left (1600\,x+{\mathrm {e}}^{x^2}\,\left (-80\,x^4-80\,x^3+96\,x^2+36\,x\right )-4\,x^4\,{\mathrm {e}}^{2\,x^2}+1000\,x^2+600\right )+1000}{x^3\,{\ln \relax (x)}^3-15\,x^3\,{\ln \relax (x)}^2+75\,x^3\,\ln \relax (x)-125\,x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1000*x - log(x)^5*(4*x + 60*x^2) - exp(x^2)*(20*x^2 - 80*x + 200*x^3 + 200*x^4) - log(x)^3*(428*x + exp(x
^2)*(2*x^2 - 40*x^4) + 620*x^2 + 8) + 4*x^2*log(x)^6 + log(x)^4*(68*x - 4*x^4*exp(x^2) + 308*x^2) + log(x)^2*(
1220*x + exp(x^2)*(4*x + 30*x^2 - 8*x^3 - 108*x^4) + 600*x^2 + 120) - exp(2*x^2)*(2*x^2 + 20*x^4) - log(x)*(16
00*x + exp(x^2)*(36*x + 96*x^2 - 80*x^3 - 80*x^4) - 4*x^4*exp(2*x^2) + 1000*x^2 + 600) + 1000)/(75*x^3*log(x)
- 15*x^3*log(x)^2 + x^3*log(x)^3 - 125*x^3),x)

[Out]

-int(-(1000*x - log(x)^5*(4*x + 60*x^2) - exp(x^2)*(20*x^2 - 80*x + 200*x^3 + 200*x^4) - log(x)^3*(428*x + exp
(x^2)*(2*x^2 - 40*x^4) + 620*x^2 + 8) + 4*x^2*log(x)^6 + log(x)^4*(68*x - 4*x^4*exp(x^2) + 308*x^2) + log(x)^2
*(1220*x + exp(x^2)*(4*x + 30*x^2 - 8*x^3 - 108*x^4) + 600*x^2 + 120) - exp(2*x^2)*(2*x^2 + 20*x^4) - log(x)*(
1600*x + exp(x^2)*(36*x + 96*x^2 - 80*x^3 - 80*x^4) - 4*x^4*exp(2*x^2) + 1000*x^2 + 600) + 1000)/(75*x^3*log(x
) - 15*x^3*log(x)^2 + x^3*log(x)^3 - 125*x^3), x)

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sympy [B]  time = 0.62, size = 121, normalized size = 4.17 \begin {gather*} \frac {\left (x \log {\relax (x )} - 5 x\right ) e^{2 x^{2}} + \left (- 2 x \log {\relax (x )}^{4} + 20 x \log {\relax (x )}^{3} - 54 x \log {\relax (x )}^{2} + 40 x \log {\relax (x )} - 100 x - 4 \log {\relax (x )}^{2} + 40 \log {\relax (x )} - 100\right ) e^{x^{2}}}{x \log {\relax (x )}^{3} - 15 x \log {\relax (x )}^{2} + 75 x \log {\relax (x )} - 125 x} + \log {\relax (x )}^{4} + \frac {\left (4 x + 4\right ) \log {\relax (x )}^{2}}{x} - \frac {- 8 x - 4}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**2*ln(x)**6+(-60*x**2-4*x)*ln(x)**5+(-4*x**4*exp(x**2)+308*x**2+68*x)*ln(x)**4+((40*x**4-2*x**2
)*exp(x**2)-620*x**2-428*x-8)*ln(x)**3+((-108*x**4-8*x**3+30*x**2+4*x)*exp(x**2)+600*x**2+1220*x+120)*ln(x)**2
+(4*x**4*exp(x**2)**2+(80*x**4+80*x**3-96*x**2-36*x)*exp(x**2)-1000*x**2-1600*x-600)*ln(x)+(-20*x**4-2*x**2)*e
xp(x**2)**2+(-200*x**4-200*x**3-20*x**2+80*x)*exp(x**2)+1000*x+1000)/(x**3*ln(x)**3-15*x**3*ln(x)**2+75*x**3*l
n(x)-125*x**3),x)

[Out]

((x*log(x) - 5*x)*exp(2*x**2) + (-2*x*log(x)**4 + 20*x*log(x)**3 - 54*x*log(x)**2 + 40*x*log(x) - 100*x - 4*lo
g(x)**2 + 40*log(x) - 100)*exp(x**2))/(x*log(x)**3 - 15*x*log(x)**2 + 75*x*log(x) - 125*x) + log(x)**4 + (4*x
+ 4)*log(x)**2/x - (-8*x - 4)/x**2

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