3.4.38 \(\int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} (-15 x-75 x^3)+e^x (2+5 x-100 x^2+25 x^3)+e^{2 e^6} (-76 x+e^x x-750 x^3-1875 x^5)+(76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} (30 x+150 x^3)) \log (x)+(-15 x-3 e^{2 e^6} x-75 x^3) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} (-15 x-75 x^3)+e^{2 e^6} (-75 x-750 x^3-1875 x^5)+(75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} (30 x+150 x^3)) \log (x)+(-15 x-3 e^{2 e^6} x-75 x^3) \log ^2(x)+x \log ^3(x)} \, dx\)

Optimal. Leaf size=30 \[ x+\frac {-e^x+x}{\left (5+e^{2 e^6}+25 x^2-\log (x)\right )^2} \]

________________________________________________________________________________________

Rubi [F]  time = 13.54, 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 {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{-125 x-e^{6 e^6} x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-132*x - E^(6*E^6)*x - 1800*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^x*(2 + 5*x - 100*
x^2 + 25*x^3) + E^(2*E^6)*(-76*x + E^x*x - 750*x^3 - 1875*x^5) + (76*x + 3*E^(4*E^6)*x - E^x*x + 750*x^3 + 187
5*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3)/(-125*x -
E^(6*E^6)*x - 1875*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^(2*E^6)*(-75*x - 750*x^3 - 187
5*x^5) + (75*x + 3*E^(4*E^6)*x + 750*x^3 + 1875*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6
)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3),x]

[Out]

x - (E^x*((5 + E^(2*E^6))*x + 25*x^3 - x*Log[x]))/(x*(5 + E^(2*E^6) + 25*x^2 - Log[x])^3) + 132*Defer[Int][(5*
(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-3), x] + 76*E^(2*E^6)*Defer[Int][(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x]
)^(-3), x] + 15*E^(4*E^6)*Defer[Int][(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-3), x] + E^(6*E^6)*Defer[Int][(
5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-3), x] + 2*(5 + E^(2*E^6))^3*Defer[Int][(5*(1 + E^(2*E^6)/5) + 25*x^2
- Log[x])^(-3), x] + 1800*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 750*E^(2*E^6)*Defer[
Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 75*E^(4*E^6)*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25
*x^2 - Log[x])^3, x] - 750*(5 + E^(2*E^6))*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 225*
(5 + E^(2*E^6))^2*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] - 150*E^(2*E^6)*(10 + E^(2*E^6)
)*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 9375*Defer[Int][x^4/(5*(1 + E^(2*E^6)/5) + 25
*x^2 - Log[x])^3, x] + 1875*E^(2*E^6)*Defer[Int][x^4/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 1875*(5 +
E^(2*E^6))*Defer[Int][x^4/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^3, x] + 62500*Defer[Int][x^6/(5*(1 + E^(2*E
^6)/5) + 25*x^2 - Log[x])^3, x] + 30*E^(2*E^6)*Defer[Int][(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-2), x] - 3
*(5 + E^(2*E^6))^2*Defer[Int][(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-2), x] + (76 + 3*E^(4*E^6))*Defer[Int]
[(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^(-2), x] + 750*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])
^2, x] + 150*E^(2*E^6)*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^2, x] - 150*(5 + E^(2*E^6))*Defe
r[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x])^2, x] + 3*(5 + E^(2*E^6))*Defer[Int][(5*(1 + E^(2*E^6)/5) +
25*x^2 - Log[x])^(-1), x] + 75*Defer[Int][x^2/(5*(1 + E^(2*E^6)/5) + 25*x^2 - Log[x]), x] + 30*E^(2*E^6)*(5 +
E^(2*E^6))*Defer[Int][(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x])^(-3), x] + (5 + E^(2*E^6))*(76 + 3*E^(4*E^6))*
Defer[Int][(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x])^(-3), x] + 75*(5 + E^(2*E^6))^2*Defer[Int][x^2/(-5*(1 + E^
(2*E^6)/5) - 25*x^2 + Log[x])^3, x] + 25*(76 + 3*E^(4*E^6))*Defer[Int][x^2/(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Lo
g[x])^3, x] + 18750*Defer[Int][x^4/(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x])^3, x] + 3750*E^(2*E^6)*Defer[Int][
x^4/(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x])^3, x] + 62500*Defer[Int][x^6/(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log
[x])^3, x] + 3*(5 + E^(2*E^6))*Defer[Int][(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x])^(-1), x] + 75*Defer[Int][x^
2/(-5*(1 + E^(2*E^6)/5) - 25*x^2 + Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-132 x-e^{6 e^6} x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{\left (-125-e^{6 e^6}\right ) x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx\\ &=\int \frac {\left (-132-e^{6 e^6}\right ) x-1800 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} \left (-76 x+e^x x-750 x^3-1875 x^5\right )+\left (76 x+3 e^{4 e^6} x-e^x x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)}{\left (-125-e^{6 e^6}\right ) x-1875 x^3-9375 x^5-15625 x^7+e^{4 e^6} \left (-15 x-75 x^3\right )+e^{2 e^6} \left (-75 x-750 x^3-1875 x^5\right )+\left (75 x+3 e^{4 e^6} x+750 x^3+1875 x^5+e^{2 e^6} \left (30 x+150 x^3\right )\right ) \log (x)+\left (-15 x-3 e^{2 e^6} x-75 x^3\right ) \log ^2(x)+x \log ^3(x)} \, dx\\ &=\int \frac {e^{6 e^6} x-e^{2 e^6+x} x+15 e^{4 e^6} x \left (1+5 x^2\right )-e^x \left (2+5 x-100 x^2+25 x^3\right )+e^{2 e^6} x \left (76+750 x^2+1875 x^4\right )+x \left (132+1800 x^2+9375 x^4+15625 x^6\right )-x \left (76+3 e^{4 e^6}-e^x+750 x^2+1875 x^4+30 e^{2 e^6} \left (1+5 x^2\right )\right ) \log (x)+3 x \left (5+e^{2 e^6}+25 x^2\right ) \log ^2(x)-x \log ^3(x)}{x \left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx\\ &=\int \left (\frac {e^{6 e^6}}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {15 e^{4 e^6} \left (1+5 x^2\right )}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {e^{2 e^6} \left (76+750 x^2+1875 x^4\right )}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {132+1800 x^2+9375 x^4+15625 x^6}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {30 e^{2 e^6} \left (-1-5 x^2\right ) \log (x)}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {3 \left (5+e^{2 e^6}+25 x^2\right ) \log ^2(x)}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}+\frac {76 \left (1+\frac {3 e^{4 e^6}}{76}\right ) \log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3}+\frac {750 x^2 \log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3}+\frac {1875 x^4 \log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3}+\frac {\log ^3(x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3}+\frac {e^x \left (-2-5 \left (1+\frac {e^{2 e^6}}{5}\right ) x+100 x^2-25 x^3+x \log (x)\right )}{x \left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3}\right ) \, dx\\ &=3 \int \frac {\left (5+e^{2 e^6}+25 x^2\right ) \log ^2(x)}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+750 \int \frac {x^2 \log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3} \, dx+1875 \int \frac {x^4 \log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3} \, dx+e^{2 e^6} \int \frac {76+750 x^2+1875 x^4}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+\left (30 e^{2 e^6}\right ) \int \frac {\left (-1-5 x^2\right ) \log (x)}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+\left (15 e^{4 e^6}\right ) \int \frac {1+5 x^2}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+e^{6 e^6} \int \frac {1}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+\left (76+3 e^{4 e^6}\right ) \int \frac {\log (x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3} \, dx+\int \frac {132+1800 x^2+9375 x^4+15625 x^6}{\left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx+\int \frac {\log ^3(x)}{\left (-5 \left (1+\frac {e^{2 e^6}}{5}\right )-25 x^2+\log (x)\right )^3} \, dx+\int \frac {e^x \left (-2-5 \left (1+\frac {e^{2 e^6}}{5}\right ) x+100 x^2-25 x^3+x \log (x)\right )}{x \left (5 \left (1+\frac {e^{2 e^6}}{5}\right )+25 x^2-\log (x)\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.15, size = 31, normalized size = 1.03 \begin {gather*} x-\frac {e^x-x}{\left (-5-e^{2 e^6}-25 x^2+\log (x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-132*x - E^(6*E^6)*x - 1800*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^x*(2 + 5*x
- 100*x^2 + 25*x^3) + E^(2*E^6)*(-76*x + E^x*x - 750*x^3 - 1875*x^5) + (76*x + 3*E^(4*E^6)*x - E^x*x + 750*x^3
+ 1875*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3)/(-1
25*x - E^(6*E^6)*x - 1875*x^3 - 9375*x^5 - 15625*x^7 + E^(4*E^6)*(-15*x - 75*x^3) + E^(2*E^6)*(-75*x - 750*x^3
- 1875*x^5) + (75*x + 3*E^(4*E^6)*x + 750*x^3 + 1875*x^5 + E^(2*E^6)*(30*x + 150*x^3))*Log[x] + (-15*x - 3*E^
(2*E^6)*x - 75*x^3)*Log[x]^2 + x*Log[x]^3),x]

[Out]

x - (E^x - x)/(-5 - E^(2*E^6) - 25*x^2 + Log[x])^2

________________________________________________________________________________________

fricas [B]  time = 0.63, size = 119, normalized size = 3.97 \begin {gather*} \frac {625 \, x^{5} + 250 \, x^{3} + x \log \relax (x)^{2} + x e^{\left (4 \, e^{6}\right )} + 10 \, {\left (5 \, x^{3} + x\right )} e^{\left (2 \, e^{6}\right )} - 2 \, {\left (25 \, x^{3} + x e^{\left (2 \, e^{6}\right )} + 5 \, x\right )} \log \relax (x) + 26 \, x - e^{x}}{625 \, x^{4} + 250 \, x^{2} + 10 \, {\left (5 \, x^{2} + 1\right )} e^{\left (2 \, e^{6}\right )} - 2 \, {\left (25 \, x^{2} + e^{\left (2 \, e^{6}\right )} + 5\right )} \log \relax (x) + \log \relax (x)^{2} + e^{\left (4 \, e^{6}\right )} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(
3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875
*x^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9375*x^5-1800*x^3-132*x)/(x*log(x)^
3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750
*x^3+75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5-750*x^3-75*x)*exp(exp(3)^2)^2-15
625*x^7-9375*x^5-1875*x^3-125*x),x, algorithm="fricas")

[Out]

(625*x^5 + 250*x^3 + x*log(x)^2 + x*e^(4*e^6) + 10*(5*x^3 + x)*e^(2*e^6) - 2*(25*x^3 + x*e^(2*e^6) + 5*x)*log(
x) + 26*x - e^x)/(625*x^4 + 250*x^2 + 10*(5*x^2 + 1)*e^(2*e^6) - 2*(25*x^2 + e^(2*e^6) + 5)*log(x) + log(x)^2
+ e^(4*e^6) + 25)

________________________________________________________________________________________

giac [B]  time = 0.59, size = 132, normalized size = 4.40 \begin {gather*} \frac {625 \, x^{5} + 50 \, x^{3} e^{\left (2 \, e^{6}\right )} - 50 \, x^{3} \log \relax (x) + 250 \, x^{3} - 2 \, x e^{\left (2 \, e^{6}\right )} \log \relax (x) + x \log \relax (x)^{2} + x e^{\left (4 \, e^{6}\right )} + 10 \, x e^{\left (2 \, e^{6}\right )} - 10 \, x \log \relax (x) + 26 \, x - e^{x}}{625 \, x^{4} + 50 \, x^{2} e^{\left (2 \, e^{6}\right )} - 50 \, x^{2} \log \relax (x) + 250 \, x^{2} - 2 \, e^{\left (2 \, e^{6}\right )} \log \relax (x) + \log \relax (x)^{2} + e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} - 10 \, \log \relax (x) + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(
3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875
*x^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9375*x^5-1800*x^3-132*x)/(x*log(x)^
3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750
*x^3+75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5-750*x^3-75*x)*exp(exp(3)^2)^2-15
625*x^7-9375*x^5-1875*x^3-125*x),x, algorithm="giac")

[Out]

(625*x^5 + 50*x^3*e^(2*e^6) - 50*x^3*log(x) + 250*x^3 - 2*x*e^(2*e^6)*log(x) + x*log(x)^2 + x*e^(4*e^6) + 10*x
*e^(2*e^6) - 10*x*log(x) + 26*x - e^x)/(625*x^4 + 50*x^2*e^(2*e^6) - 50*x^2*log(x) + 250*x^2 - 2*e^(2*e^6)*log
(x) + log(x)^2 + e^(4*e^6) + 10*e^(2*e^6) - 10*log(x) + 25)

________________________________________________________________________________________

maple [A]  time = 0.13, size = 28, normalized size = 0.93

method	result	size
risch	\(x +\frac {x -{\mathrm e}^{x}}{\left (25 x^{2}+5-\ln \relax (x )+{\mathrm e}^{2 \,{\mathrm e}^{6}}\right )^{2}}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*ln(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*ln(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2-
exp(x)*x+1875*x^5+750*x^3+76*x)*ln(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875*x^5-750*
x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9375*x^5-1800*x^3-132*x)/(x*ln(x)^3+(-3*x*ex
p(exp(3)^2)^2-75*x^3-15*x)*ln(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750*x^3+75*x)*
ln(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5-750*x^3-75*x)*exp(exp(3)^2)^2-15625*x^7-9375
*x^5-1875*x^3-125*x),x,method=_RETURNVERBOSE)

[Out]

x+(x-exp(x))/(25*x^2+5-ln(x)+exp(2*exp(6)))^2

________________________________________________________________________________________

maxima [B]  time = 0.63, size = 117, normalized size = 3.90 \begin {gather*} \frac {625 \, x^{5} + 50 \, x^{3} {\left (e^{\left (2 \, e^{6}\right )} + 5\right )} + x \log \relax (x)^{2} + x {\left (e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} + 26\right )} - 2 \, {\left (25 \, x^{3} + x {\left (e^{\left (2 \, e^{6}\right )} + 5\right )}\right )} \log \relax (x) - e^{x}}{625 \, x^{4} + 50 \, x^{2} {\left (e^{\left (2 \, e^{6}\right )} + 5\right )} - 2 \, {\left (25 \, x^{2} + e^{\left (2 \, e^{6}\right )} + 5\right )} \log \relax (x) + \log \relax (x)^{2} + e^{\left (4 \, e^{6}\right )} + 10 \, e^{\left (2 \, e^{6}\right )} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*log(x)^3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(
3)^2)^2-exp(x)*x+1875*x^5+750*x^3+76*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(exp(x)*x-1875
*x^5-750*x^3-76*x)*exp(exp(3)^2)^2+(25*x^3-100*x^2+5*x+2)*exp(x)-15625*x^7-9375*x^5-1800*x^3-132*x)/(x*log(x)^
3+(-3*x*exp(exp(3)^2)^2-75*x^3-15*x)*log(x)^2+(3*x*exp(exp(3)^2)^4+(150*x^3+30*x)*exp(exp(3)^2)^2+1875*x^5+750
*x^3+75*x)*log(x)-x*exp(exp(3)^2)^6+(-75*x^3-15*x)*exp(exp(3)^2)^4+(-1875*x^5-750*x^3-75*x)*exp(exp(3)^2)^2-15
625*x^7-9375*x^5-1875*x^3-125*x),x, algorithm="maxima")

[Out]

(625*x^5 + 50*x^3*(e^(2*e^6) + 5) + x*log(x)^2 + x*(e^(4*e^6) + 10*e^(2*e^6) + 26) - 2*(25*x^3 + x*(e^(2*e^6)
+ 5))*log(x) - e^x)/(625*x^4 + 50*x^2*(e^(2*e^6) + 5) - 2*(25*x^2 + e^(2*e^6) + 5)*log(x) + log(x)^2 + e^(4*e^
6) + 10*e^(2*e^6) + 25)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {132\,x+x\,{\mathrm {e}}^{6\,{\mathrm {e}}^6}+{\ln \relax (x)}^2\,\left (15\,x+3\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^6}+75\,x^3\right )-x\,{\ln \relax (x)}^3-\ln \relax (x)\,\left (76\,x+3\,x\,{\mathrm {e}}^{4\,{\mathrm {e}}^6}-x\,{\mathrm {e}}^x+750\,x^3+1875\,x^5+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (150\,x^3+30\,x\right )\right )+1800\,x^3+9375\,x^5+15625\,x^7-{\mathrm {e}}^x\,\left (25\,x^3-100\,x^2+5\,x+2\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (76\,x-x\,{\mathrm {e}}^x+750\,x^3+1875\,x^5\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^6}\,\left (75\,x^3+15\,x\right )}{125\,x+x\,{\mathrm {e}}^{6\,{\mathrm {e}}^6}+{\ln \relax (x)}^2\,\left (15\,x+3\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^6}+75\,x^3\right )-x\,{\ln \relax (x)}^3+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (1875\,x^5+750\,x^3+75\,x\right )+1875\,x^3+9375\,x^5+15625\,x^7-\ln \relax (x)\,\left (75\,x+3\,x\,{\mathrm {e}}^{4\,{\mathrm {e}}^6}+750\,x^3+1875\,x^5+{\mathrm {e}}^{2\,{\mathrm {e}}^6}\,\left (150\,x^3+30\,x\right )\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^6}\,\left (75\,x^3+15\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((132*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 - log(x)*(76*x + 3*x*
exp(4*exp(6)) - x*exp(x) + 750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + 1800*x^3 + 9375*x^5 + 15625*
x^7 - exp(x)*(5*x - 100*x^2 + 25*x^3 + 2) + exp(2*exp(6))*(76*x - x*exp(x) + 750*x^3 + 1875*x^5) + exp(4*exp(6
))*(15*x + 75*x^3))/(125*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 + exp
(2*exp(6))*(75*x + 750*x^3 + 1875*x^5) + 1875*x^3 + 9375*x^5 + 15625*x^7 - log(x)*(75*x + 3*x*exp(4*exp(6)) +
750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + exp(4*exp(6))*(15*x + 75*x^3)),x)

[Out]

int((132*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 - log(x)*(76*x + 3*x*
exp(4*exp(6)) - x*exp(x) + 750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + 1800*x^3 + 9375*x^5 + 15625*
x^7 - exp(x)*(5*x - 100*x^2 + 25*x^3 + 2) + exp(2*exp(6))*(76*x - x*exp(x) + 750*x^3 + 1875*x^5) + exp(4*exp(6
))*(15*x + 75*x^3))/(125*x + x*exp(6*exp(6)) + log(x)^2*(15*x + 3*x*exp(2*exp(6)) + 75*x^3) - x*log(x)^3 + exp
(2*exp(6))*(75*x + 750*x^3 + 1875*x^5) + 1875*x^3 + 9375*x^5 + 15625*x^7 - log(x)*(75*x + 3*x*exp(4*exp(6)) +
750*x^3 + 1875*x^5 + exp(2*exp(6))*(30*x + 150*x^3)) + exp(4*exp(6))*(15*x + 75*x^3)), x)

________________________________________________________________________________________

sympy [B]  time = 0.74, size = 139, normalized size = 4.63 \begin {gather*} x + \frac {x}{625 x^{4} + 250 x^{2} + 50 x^{2} e^{2 e^{6}} + \left (- 50 x^{2} - 10 - 2 e^{2 e^{6}}\right ) \log {\relax (x )} + \log {\relax (x )}^{2} + 25 + 10 e^{2 e^{6}} + e^{4 e^{6}}} - \frac {e^{x}}{625 x^{4} - 50 x^{2} \log {\relax (x )} + 250 x^{2} + 50 x^{2} e^{2 e^{6}} + \log {\relax (x )}^{2} - 10 \log {\relax (x )} - 2 e^{2 e^{6}} \log {\relax (x )} + 25 + 10 e^{2 e^{6}} + e^{4 e^{6}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*ln(x)**3+(-3*x*exp(exp(3)**2)**2-75*x**3-15*x)*ln(x)**2+(3*x*exp(exp(3)**2)**4+(150*x**3+30*x)*ex
p(exp(3)**2)**2-exp(x)*x+1875*x**5+750*x**3+76*x)*ln(x)-x*exp(exp(3)**2)**6+(-75*x**3-15*x)*exp(exp(3)**2)**4+
(exp(x)*x-1875*x**5-750*x**3-76*x)*exp(exp(3)**2)**2+(25*x**3-100*x**2+5*x+2)*exp(x)-15625*x**7-9375*x**5-1800
*x**3-132*x)/(x*ln(x)**3+(-3*x*exp(exp(3)**2)**2-75*x**3-15*x)*ln(x)**2+(3*x*exp(exp(3)**2)**4+(150*x**3+30*x)
*exp(exp(3)**2)**2+1875*x**5+750*x**3+75*x)*ln(x)-x*exp(exp(3)**2)**6+(-75*x**3-15*x)*exp(exp(3)**2)**4+(-1875
*x**5-750*x**3-75*x)*exp(exp(3)**2)**2-15625*x**7-9375*x**5-1875*x**3-125*x),x)

[Out]

x + x/(625*x**4 + 250*x**2 + 50*x**2*exp(2*exp(6)) + (-50*x**2 - 10 - 2*exp(2*exp(6)))*log(x) + log(x)**2 + 25
+ 10*exp(2*exp(6)) + exp(4*exp(6))) - exp(x)/(625*x**4 - 50*x**2*log(x) + 250*x**2 + 50*x**2*exp(2*exp(6)) +
log(x)**2 - 10*log(x) - 2*exp(2*exp(6))*log(x) + 25 + 10*exp(2*exp(6)) + exp(4*exp(6)))

________________________________________________________________________________________