3.42.11 \(\int \frac {e^2 (-200-300 x)+48 x-104 x^2+40 x^3+24 x^4-12 x^5+e (-80-200 x-160 x^2+120 x^3)+(160+128 x+100 e^2 x+192 x^2-112 x^3-16 x^4+4 x^5+e (400+560 x+80 x^2-40 x^3)) \log (x)+(-200-260 x-200 e x-80 x^2+40 x^3) \log ^2(x)+100 x \log ^3(x)}{25 e^2 x^3+4 x^5-4 x^6+x^7+e (20 x^4-10 x^5)+(50 e^2 x^2-12 x^4+2 x^5+2 x^6+e (-10 x^3-20 x^4)) \log (x)+(25 e^2 x-11 x^3+16 x^4+x^5+e (-80 x^2-10 x^3)) \log ^2(x)+(-50 e x+30 x^2+10 x^3) \log ^3(x)+25 x \log ^4(x)} \, dx\)

Optimal. Leaf size=32 \[ \frac {4 \left (2+x+\frac {2}{x-\frac {5 (-e+\log (x))}{2-x}}\right )}{x+\log (x)} \]

________________________________________________________________________________________

Rubi [F]  time = 6.96, 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^2 (-200-300 x)+48 x-104 x^2+40 x^3+24 x^4-12 x^5+e \left (-80-200 x-160 x^2+120 x^3\right )+\left (160+128 x+100 e^2 x+192 x^2-112 x^3-16 x^4+4 x^5+e \left (400+560 x+80 x^2-40 x^3\right )\right ) \log (x)+\left (-200-260 x-200 e x-80 x^2+40 x^3\right ) \log ^2(x)+100 x \log ^3(x)}{25 e^2 x^3+4 x^5-4 x^6+x^7+e \left (20 x^4-10 x^5\right )+\left (50 e^2 x^2-12 x^4+2 x^5+2 x^6+e \left (-10 x^3-20 x^4\right )\right ) \log (x)+\left (25 e^2 x-11 x^3+16 x^4+x^5+e \left (-80 x^2-10 x^3\right )\right ) \log ^2(x)+\left (-50 e x+30 x^2+10 x^3\right ) \log ^3(x)+25 x \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^2*(-200 - 300*x) + 48*x - 104*x^2 + 40*x^3 + 24*x^4 - 12*x^5 + E*(-80 - 200*x - 160*x^2 + 120*x^3) + (1
60 + 128*x + 100*E^2*x + 192*x^2 - 112*x^3 - 16*x^4 + 4*x^5 + E*(400 + 560*x + 80*x^2 - 40*x^3))*Log[x] + (-20
0 - 260*x - 200*E*x - 80*x^2 + 40*x^3)*Log[x]^2 + 100*x*Log[x]^3)/(25*E^2*x^3 + 4*x^5 - 4*x^6 + x^7 + E*(20*x^
4 - 10*x^5) + (50*E^2*x^2 - 12*x^4 + 2*x^5 + 2*x^6 + E*(-10*x^3 - 20*x^4))*Log[x] + (25*E^2*x - 11*x^3 + 16*x^
4 + x^5 + E*(-80*x^2 - 10*x^3))*Log[x]^2 + (-50*E*x + 30*x^2 + 10*x^3)*Log[x]^3 + 25*x*Log[x]^4),x]

[Out]

80*Defer[Int][(5*E + 2*x - x^2 - 5*Log[x])^(-2), x] + (80*(1 - 4*E)*(1 - 7/Sqrt[49 + 20*E])*Defer[Int][1/((7 -
Sqrt[49 + 20*E] - 2*x)*(5*E + 2*x - x^2 - 5*Log[x])^2), x])/E - (80*(14 + E*(9 + 10*E))*Defer[Int][1/((7 + Sq
rt[49 + 20*E] - 2*x)*(5*E + 2*x - x^2 - 5*Log[x])^2), x])/(E*Sqrt[49 + 20*E]) + (80*(1 - 4*E)*(1 + 7/Sqrt[49 +
20*E])*Defer[Int][1/((7 + Sqrt[49 + 20*E] - 2*x)*(5*E + 2*x - x^2 - 5*Log[x])^2), x])/E + (80*Defer[Int][1/(x
*(5*E + 2*x - x^2 - 5*Log[x])^2), x])/E - (80*(14 + E*(9 + 10*E))*Defer[Int][1/((-7 + Sqrt[49 + 20*E] + 2*x)*(
5*E + 2*x - x^2 - 5*Log[x])^2), x])/(E*Sqrt[49 + 20*E]) + (80*Defer[Int][1/((7 + Sqrt[49 + 20*E] - 2*x)*(5*E +
2*x - x^2 - 5*Log[x])), x])/Sqrt[49 + 20*E] + (80*Defer[Int][1/((-7 + Sqrt[49 + 20*E] + 2*x)*(5*E + 2*x - x^2
- 5*Log[x])), x])/Sqrt[49 + 20*E] - 80*(7 + 5*E)*Defer[Int][1/((5*E + 7*x - x^2)^2*(5*E + 2*x - x^2 - 5*Log[x
])), x] - 120*Defer[Int][x/((5*E + 7*x - x^2)^2*(5*E + 2*x - x^2 - 5*Log[x])), x] - 12*Defer[Int][(x + Log[x])
^(-2), x] - (8*(2 - 5*E)*(1 - 7/Sqrt[49 + 20*E])*Defer[Int][1/((7 - Sqrt[49 + 20*E] - 2*x)*(x + Log[x])^2), x]
)/(5*E) + (16*(14 - 5*E)*Defer[Int][1/((7 + Sqrt[49 + 20*E] - 2*x)*(x + Log[x])^2), x])/(5*E*Sqrt[49 + 20*E])
- (8*(2 - 5*E)*(1 + 7/Sqrt[49 + 20*E])*Defer[Int][1/((7 + Sqrt[49 + 20*E] - 2*x)*(x + Log[x])^2), x])/(5*E) -
(8*(2 + 5*E)*Defer[Int][1/(x*(x + Log[x])^2), x])/(5*E) - 4*Defer[Int][x/(x + Log[x])^2, x] + (16*(14 - 5*E)*D
efer[Int][1/((-7 + Sqrt[49 + 20*E] + 2*x)*(x + Log[x])^2), x])/(5*E*Sqrt[49 + 20*E]) + 4*Defer[Int][(x + Log[x
])^(-1), x] + (16*Defer[Int][1/((7 + Sqrt[49 + 20*E] - 2*x)*(x + Log[x])), x])/Sqrt[49 + 20*E] + (16*Defer[Int
][1/((-7 + Sqrt[49 + 20*E] + 2*x)*(x + Log[x])), x])/Sqrt[49 + 20*E] - 16*(7 + 5*E)*Defer[Int][1/((5*E + 7*x -
x^2)^2*(x + Log[x])), x] - 24*Defer[Int][x/((5*E + 7*x - x^2)^2*(x + Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-25 e^2 (2+3 x)+10 e \left (-2-5 x-4 x^2+3 x^3\right )+x \left (12-26 x+10 x^2+6 x^3-3 x^4\right )+\left (40+32 x+25 e^2 x+48 x^2-28 x^3-4 x^4+x^5-10 e \left (-10-14 x-2 x^2+x^3\right )\right ) \log (x)-5 \left (10+(13+10 e) x+4 x^2-2 x^3\right ) \log ^2(x)+25 x \log ^3(x)\right )}{x (5 e-(-2+x) x-5 \log (x))^2 (x+\log (x))^2} \, dx\\ &=4 \int \frac {-25 e^2 (2+3 x)+10 e \left (-2-5 x-4 x^2+3 x^3\right )+x \left (12-26 x+10 x^2+6 x^3-3 x^4\right )+\left (40+32 x+25 e^2 x+48 x^2-28 x^3-4 x^4+x^5-10 e \left (-10-14 x-2 x^2+x^3\right )\right ) \log (x)-5 \left (10+(13+10 e) x+4 x^2-2 x^3\right ) \log ^2(x)+25 x \log ^3(x)}{x (5 e-(-2+x) x-5 \log (x))^2 (x+\log (x))^2} \, dx\\ &=4 \int \left (-\frac {10 \left (14+5 e-4 x+x^2\right )}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )}+\frac {(1+x) \left (-2 (2+5 e)-(12+5 e) x-5 x^2+x^3\right )}{x \left (5 e+7 x-x^2\right ) (x+\log (x))^2}+\frac {-28-10 e+25 e^2+2 (4+35 e) x+(47-10 e) x^2-14 x^3+x^4}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))}+\frac {10 \left (-10+9 x-6 x^2+2 x^3\right )}{x \left (-5 e-7 x+x^2\right ) \left (-5 e-2 x+x^2+5 \log (x)\right )^2}\right ) \, dx\\ &=4 \int \frac {(1+x) \left (-2 (2+5 e)-(12+5 e) x-5 x^2+x^3\right )}{x \left (5 e+7 x-x^2\right ) (x+\log (x))^2} \, dx+4 \int \frac {-28-10 e+25 e^2+2 (4+35 e) x+(47-10 e) x^2-14 x^3+x^4}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx-40 \int \frac {14+5 e-4 x+x^2}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+40 \int \frac {-10+9 x-6 x^2+2 x^3}{x \left (-5 e-7 x+x^2\right ) \left (-5 e-2 x+x^2+5 \log (x)\right )^2} \, dx\\ &=4 \int \left (-\frac {3}{(x+\log (x))^2}-\frac {2 (2+5 e)}{5 e x (x+\log (x))^2}-\frac {x}{(x+\log (x))^2}+\frac {2 (14-5 e-(2-5 e) x)}{5 e \left (5 e+7 x-x^2\right ) (x+\log (x))^2}\right ) \, dx+4 \int \left (\frac {1}{x+\log (x)}-\frac {2 (14+10 e+3 x)}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))}+\frac {2}{\left (5 e+7 x-x^2\right ) (x+\log (x))}\right ) \, dx+40 \int \left (\frac {2}{\left (5 e+2 x-x^2-5 \log (x)\right )^2}+\frac {2}{e x \left (5 e+2 x-x^2-5 \log (x)\right )^2}+\frac {-14-9 e-10 e^2+2 (1-4 e) x}{e \left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}\right ) \, dx-40 \int \left (\frac {14+10 e+3 x}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )}-\frac {1}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )}\right ) \, dx\\ &=-\left (4 \int \frac {x}{(x+\log (x))^2} \, dx\right )+4 \int \frac {1}{x+\log (x)} \, dx-8 \int \frac {14+10 e+3 x}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx+8 \int \frac {1}{\left (5 e+7 x-x^2\right ) (x+\log (x))} \, dx-12 \int \frac {1}{(x+\log (x))^2} \, dx-40 \int \frac {14+10 e+3 x}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+40 \int \frac {1}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+80 \int \frac {1}{\left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx+\frac {8 \int \frac {14-5 e-(2-5 e) x}{\left (5 e+7 x-x^2\right ) (x+\log (x))^2} \, dx}{5 e}+\frac {40 \int \frac {-14-9 e-10 e^2+2 (1-4 e) x}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}+\frac {80 \int \frac {1}{x \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}-\frac {(8 (2+5 e)) \int \frac {1}{x (x+\log (x))^2} \, dx}{5 e}\\ &=-\left (4 \int \frac {x}{(x+\log (x))^2} \, dx\right )+4 \int \frac {1}{x+\log (x)} \, dx+8 \int \left (\frac {2}{\sqrt {49+20 e} \left (7+\sqrt {49+20 e}-2 x\right ) (x+\log (x))}+\frac {2}{\sqrt {49+20 e} \left (-7+\sqrt {49+20 e}+2 x\right ) (x+\log (x))}\right ) \, dx-8 \int \left (\frac {14 \left (1+\frac {5 e}{7}\right )}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))}+\frac {3 x}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))}\right ) \, dx-12 \int \frac {1}{(x+\log (x))^2} \, dx+40 \int \left (\frac {2}{\sqrt {49+20 e} \left (7+\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )}+\frac {2}{\sqrt {49+20 e} \left (-7+\sqrt {49+20 e}+2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )}\right ) \, dx-40 \int \left (\frac {14 \left (1+\frac {5 e}{7}\right )}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )}+\frac {3 x}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )}\right ) \, dx+80 \int \frac {1}{\left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx+\frac {8 \int \left (\frac {14 \left (1-\frac {5 e}{14}\right )}{\left (5 e+7 x-x^2\right ) (x+\log (x))^2}+\frac {(-2+5 e) x}{\left (5 e+7 x-x^2\right ) (x+\log (x))^2}\right ) \, dx}{5 e}+\frac {40 \int \left (-\frac {14 \left (1+\frac {1}{14} e (9+10 e)\right )}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}-\frac {2 (-1+4 e) x}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}\right ) \, dx}{e}+\frac {80 \int \frac {1}{x \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}-\frac {(8 (2+5 e)) \int \frac {1}{x (x+\log (x))^2} \, dx}{5 e}\\ &=-\left (4 \int \frac {x}{(x+\log (x))^2} \, dx\right )+4 \int \frac {1}{x+\log (x)} \, dx-12 \int \frac {1}{(x+\log (x))^2} \, dx-24 \int \frac {x}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx+80 \int \frac {1}{\left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx-120 \int \frac {x}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+\frac {80 \int \frac {1}{x \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}+\frac {(8 (14-5 e)) \int \frac {1}{\left (5 e+7 x-x^2\right ) (x+\log (x))^2} \, dx}{5 e}+\frac {(80 (1-4 e)) \int \frac {x}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}+\frac {(8 (-2+5 e)) \int \frac {x}{\left (5 e+7 x-x^2\right ) (x+\log (x))^2} \, dx}{5 e}-\frac {(8 (2+5 e)) \int \frac {1}{x (x+\log (x))^2} \, dx}{5 e}-(16 (7+5 e)) \int \frac {1}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx-(80 (7+5 e)) \int \frac {1}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+\frac {16 \int \frac {1}{\left (7+\sqrt {49+20 e}-2 x\right ) (x+\log (x))} \, dx}{\sqrt {49+20 e}}+\frac {16 \int \frac {1}{\left (-7+\sqrt {49+20 e}+2 x\right ) (x+\log (x))} \, dx}{\sqrt {49+20 e}}+\frac {80 \int \frac {1}{\left (7+\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx}{\sqrt {49+20 e}}+\frac {80 \int \frac {1}{\left (-7+\sqrt {49+20 e}+2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx}{\sqrt {49+20 e}}-\frac {(40 (14+e (9+10 e))) \int \frac {1}{\left (5 e+7 x-x^2\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}\\ &=-\left (4 \int \frac {x}{(x+\log (x))^2} \, dx\right )+4 \int \frac {1}{x+\log (x)} \, dx-12 \int \frac {1}{(x+\log (x))^2} \, dx-24 \int \frac {x}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx+80 \int \frac {1}{\left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx-120 \int \frac {x}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+\frac {80 \int \frac {1}{x \left (5 e+2 x-x^2-5 \log (x)\right )^2} \, dx}{e}+\frac {(8 (14-5 e)) \int \left (\frac {2}{\sqrt {49+20 e} \left (7+\sqrt {49+20 e}-2 x\right ) (x+\log (x))^2}+\frac {2}{\sqrt {49+20 e} \left (-7+\sqrt {49+20 e}+2 x\right ) (x+\log (x))^2}\right ) \, dx}{5 e}+\frac {(80 (1-4 e)) \int \left (\frac {1-\frac {7}{\sqrt {49+20 e}}}{\left (7-\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}+\frac {1+\frac {7}{\sqrt {49+20 e}}}{\left (7+\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}\right ) \, dx}{e}+\frac {(8 (-2+5 e)) \int \left (\frac {1-\frac {7}{\sqrt {49+20 e}}}{\left (7-\sqrt {49+20 e}-2 x\right ) (x+\log (x))^2}+\frac {1+\frac {7}{\sqrt {49+20 e}}}{\left (7+\sqrt {49+20 e}-2 x\right ) (x+\log (x))^2}\right ) \, dx}{5 e}-\frac {(8 (2+5 e)) \int \frac {1}{x (x+\log (x))^2} \, dx}{5 e}-(16 (7+5 e)) \int \frac {1}{\left (5 e+7 x-x^2\right )^2 (x+\log (x))} \, dx-(80 (7+5 e)) \int \frac {1}{\left (5 e+7 x-x^2\right )^2 \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx+\frac {16 \int \frac {1}{\left (7+\sqrt {49+20 e}-2 x\right ) (x+\log (x))} \, dx}{\sqrt {49+20 e}}+\frac {16 \int \frac {1}{\left (-7+\sqrt {49+20 e}+2 x\right ) (x+\log (x))} \, dx}{\sqrt {49+20 e}}+\frac {80 \int \frac {1}{\left (7+\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx}{\sqrt {49+20 e}}+\frac {80 \int \frac {1}{\left (-7+\sqrt {49+20 e}+2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )} \, dx}{\sqrt {49+20 e}}-\frac {(40 (14+e (9+10 e))) \int \left (\frac {2}{\sqrt {49+20 e} \left (7+\sqrt {49+20 e}-2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}+\frac {2}{\sqrt {49+20 e} \left (-7+\sqrt {49+20 e}+2 x\right ) \left (5 e+2 x-x^2-5 \log (x)\right )^2}\right ) \, dx}{e}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.13, size = 47, normalized size = 1.47 \begin {gather*} \frac {4 \left (4+2 x-x^3+5 e (2+x)-5 (2+x) \log (x)\right )}{(5 e-(-2+x) x-5 \log (x)) (x+\log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^2*(-200 - 300*x) + 48*x - 104*x^2 + 40*x^3 + 24*x^4 - 12*x^5 + E*(-80 - 200*x - 160*x^2 + 120*x^3
) + (160 + 128*x + 100*E^2*x + 192*x^2 - 112*x^3 - 16*x^4 + 4*x^5 + E*(400 + 560*x + 80*x^2 - 40*x^3))*Log[x]
+ (-200 - 260*x - 200*E*x - 80*x^2 + 40*x^3)*Log[x]^2 + 100*x*Log[x]^3)/(25*E^2*x^3 + 4*x^5 - 4*x^6 + x^7 + E*
(20*x^4 - 10*x^5) + (50*E^2*x^2 - 12*x^4 + 2*x^5 + 2*x^6 + E*(-10*x^3 - 20*x^4))*Log[x] + (25*E^2*x - 11*x^3 +
16*x^4 + x^5 + E*(-80*x^2 - 10*x^3))*Log[x]^2 + (-50*E*x + 30*x^2 + 10*x^3)*Log[x]^3 + 25*x*Log[x]^4),x]

[Out]

(4*(4 + 2*x - x^3 + 5*E*(2 + x) - 5*(2 + x)*Log[x]))/((5*E - (-2 + x)*x - 5*Log[x])*(x + Log[x]))

________________________________________________________________________________________

fricas [A]  time = 0.69, size = 60, normalized size = 1.88 \begin {gather*} \frac {4 \, {\left (x^{3} - 5 \, {\left (x + 2\right )} e + 5 \, {\left (x + 2\right )} \log \relax (x) - 2 \, x - 4\right )}}{x^{3} - 2 \, x^{2} - 5 \, x e + {\left (x^{2} + 3 \, x - 5 \, e\right )} \log \relax (x) + 5 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((100*x*log(x)^3+(-200*x*exp(1)+40*x^3-80*x^2-260*x-200)*log(x)^2+(100*x*exp(1)^2+(-40*x^3+80*x^2+560
*x+400)*exp(1)+4*x^5-16*x^4-112*x^3+192*x^2+128*x+160)*log(x)+(-300*x-200)*exp(1)^2+(120*x^3-160*x^2-200*x-80)
*exp(1)-12*x^5+24*x^4+40*x^3-104*x^2+48*x)/(25*x*log(x)^4+(-50*x*exp(1)+10*x^3+30*x^2)*log(x)^3+(25*x*exp(1)^2
+(-10*x^3-80*x^2)*exp(1)+x^5+16*x^4-11*x^3)*log(x)^2+(50*x^2*exp(1)^2+(-20*x^4-10*x^3)*exp(1)+2*x^6+2*x^5-12*x
^4)*log(x)+25*x^3*exp(1)^2+(-10*x^5+20*x^4)*exp(1)+x^7-4*x^6+4*x^5),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

giac [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((100*x*log(x)^3+(-200*x*exp(1)+40*x^3-80*x^2-260*x-200)*log(x)^2+(100*x*exp(1)^2+(-40*x^3+80*x^2+560
*x+400)*exp(1)+4*x^5-16*x^4-112*x^3+192*x^2+128*x+160)*log(x)+(-300*x-200)*exp(1)^2+(120*x^3-160*x^2-200*x-80)
*exp(1)-12*x^5+24*x^4+40*x^3-104*x^2+48*x)/(25*x*log(x)^4+(-50*x*exp(1)+10*x^3+30*x^2)*log(x)^3+(25*x*exp(1)^2
+(-10*x^3-80*x^2)*exp(1)+x^5+16*x^4-11*x^3)*log(x)^2+(50*x^2*exp(1)^2+(-20*x^4-10*x^3)*exp(1)+2*x^6+2*x^5-12*x
^4)*log(x)+25*x^3*exp(1)^2+(-10*x^5+20*x^4)*exp(1)+x^7-4*x^6+4*x^5),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [B]  time = 0.04, size = 73, normalized size = 2.28

method	result	size
risch	\(\frac {-4 x^{3}+20 x \,{\mathrm e}-20 x \ln \relax (x )+40 \,{\mathrm e}+8 x -40 \ln \relax (x )+16}{-x^{3}-x^{2} \ln \relax (x )+5 x \,{\mathrm e}+5 \,{\mathrm e} \ln \relax (x )+2 x^{2}-3 x \ln \relax (x )-5 \ln \relax (x )^{2}}\)	\(73\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((100*x*ln(x)^3+(-200*x*exp(1)+40*x^3-80*x^2-260*x-200)*ln(x)^2+(100*x*exp(1)^2+(-40*x^3+80*x^2+560*x+400)*
exp(1)+4*x^5-16*x^4-112*x^3+192*x^2+128*x+160)*ln(x)+(-300*x-200)*exp(1)^2+(120*x^3-160*x^2-200*x-80)*exp(1)-1
2*x^5+24*x^4+40*x^3-104*x^2+48*x)/(25*x*ln(x)^4+(-50*x*exp(1)+10*x^3+30*x^2)*ln(x)^3+(25*x*exp(1)^2+(-10*x^3-8
0*x^2)*exp(1)+x^5+16*x^4-11*x^3)*ln(x)^2+(50*x^2*exp(1)^2+(-20*x^4-10*x^3)*exp(1)+2*x^6+2*x^5-12*x^4)*ln(x)+25
*x^3*exp(1)^2+(-10*x^5+20*x^4)*exp(1)+x^7-4*x^6+4*x^5),x,method=_RETURNVERBOSE)

[Out]

4*(-x^3+5*x*exp(1)-5*x*ln(x)+10*exp(1)+2*x-10*ln(x)+4)/(-x^3-x^2*ln(x)+5*x*exp(1)+5*exp(1)*ln(x)+2*x^2-3*x*ln(
x)-5*ln(x)^2)

________________________________________________________________________________________

maxima [B]  time = 0.46, size = 63, normalized size = 1.97 \begin {gather*} \frac {4 \, {\left (x^{3} - x {\left (5 \, e + 2\right )} + 5 \, {\left (x + 2\right )} \log \relax (x) - 10 \, e - 4\right )}}{x^{3} - 2 \, x^{2} - 5 \, x e + {\left (x^{2} + 3 \, x - 5 \, e\right )} \log \relax (x) + 5 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((100*x*log(x)^3+(-200*x*exp(1)+40*x^3-80*x^2-260*x-200)*log(x)^2+(100*x*exp(1)^2+(-40*x^3+80*x^2+560
*x+400)*exp(1)+4*x^5-16*x^4-112*x^3+192*x^2+128*x+160)*log(x)+(-300*x-200)*exp(1)^2+(120*x^3-160*x^2-200*x-80)
*exp(1)-12*x^5+24*x^4+40*x^3-104*x^2+48*x)/(25*x*log(x)^4+(-50*x*exp(1)+10*x^3+30*x^2)*log(x)^3+(25*x*exp(1)^2
+(-10*x^3-80*x^2)*exp(1)+x^5+16*x^4-11*x^3)*log(x)^2+(50*x^2*exp(1)^2+(-20*x^4-10*x^3)*exp(1)+2*x^6+2*x^5-12*x
^4)*log(x)+25*x^3*exp(1)^2+(-10*x^5+20*x^4)*exp(1)+x^7-4*x^6+4*x^5),x, algorithm="maxima")

[Out]

4*(x^3 - x*(5*e + 2) + 5*(x + 2)*log(x) - 10*e - 4)/(x^3 - 2*x^2 - 5*x*e + (x^2 + 3*x - 5*e)*log(x) + 5*log(x)
^2)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {48\,x+100\,x\,{\ln \relax (x)}^3-\mathrm {e}\,\left (-120\,x^3+160\,x^2+200\,x+80\right )-{\ln \relax (x)}^2\,\left (260\,x+200\,x\,\mathrm {e}+80\,x^2-40\,x^3+200\right )-104\,x^2+40\,x^3+24\,x^4-12\,x^5-{\mathrm {e}}^2\,\left (300\,x+200\right )+\ln \relax (x)\,\left (128\,x+100\,x\,{\mathrm {e}}^2+\mathrm {e}\,\left (-40\,x^3+80\,x^2+560\,x+400\right )+192\,x^2-112\,x^3-16\,x^4+4\,x^5+160\right )}{{\ln \relax (x)}^2\,\left (25\,x\,{\mathrm {e}}^2-\mathrm {e}\,\left (10\,x^3+80\,x^2\right )-11\,x^3+16\,x^4+x^5\right )+25\,x\,{\ln \relax (x)}^4+\ln \relax (x)\,\left (50\,x^2\,{\mathrm {e}}^2-\mathrm {e}\,\left (20\,x^4+10\,x^3\right )-12\,x^4+2\,x^5+2\,x^6\right )+\mathrm {e}\,\left (20\,x^4-10\,x^5\right )+25\,x^3\,{\mathrm {e}}^2+{\ln \relax (x)}^3\,\left (10\,x^3+30\,x^2-50\,\mathrm {e}\,x\right )+4\,x^5-4\,x^6+x^7} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((48*x + 100*x*log(x)^3 - exp(1)*(200*x + 160*x^2 - 120*x^3 + 80) - log(x)^2*(260*x + 200*x*exp(1) + 80*x^2
- 40*x^3 + 200) - 104*x^2 + 40*x^3 + 24*x^4 - 12*x^5 - exp(2)*(300*x + 200) + log(x)*(128*x + 100*x*exp(2) +
exp(1)*(560*x + 80*x^2 - 40*x^3 + 400) + 192*x^2 - 112*x^3 - 16*x^4 + 4*x^5 + 160))/(log(x)^2*(25*x*exp(2) - e
xp(1)*(80*x^2 + 10*x^3) - 11*x^3 + 16*x^4 + x^5) + 25*x*log(x)^4 + log(x)*(50*x^2*exp(2) - exp(1)*(10*x^3 + 20
*x^4) - 12*x^4 + 2*x^5 + 2*x^6) + exp(1)*(20*x^4 - 10*x^5) + 25*x^3*exp(2) + log(x)^3*(30*x^2 - 50*x*exp(1) +
10*x^3) + 4*x^5 - 4*x^6 + x^7),x)

[Out]

int((48*x + 100*x*log(x)^3 - exp(1)*(200*x + 160*x^2 - 120*x^3 + 80) - log(x)^2*(260*x + 200*x*exp(1) + 80*x^2
- 40*x^3 + 200) - 104*x^2 + 40*x^3 + 24*x^4 - 12*x^5 - exp(2)*(300*x + 200) + log(x)*(128*x + 100*x*exp(2) +
exp(1)*(560*x + 80*x^2 - 40*x^3 + 400) + 192*x^2 - 112*x^3 - 16*x^4 + 4*x^5 + 160))/(log(x)^2*(25*x*exp(2) - e
xp(1)*(80*x^2 + 10*x^3) - 11*x^3 + 16*x^4 + x^5) + 25*x*log(x)^4 + log(x)*(50*x^2*exp(2) - exp(1)*(10*x^3 + 20
*x^4) - 12*x^4 + 2*x^5 + 2*x^6) + exp(1)*(20*x^4 - 10*x^5) + 25*x^3*exp(2) + log(x)^3*(30*x^2 - 50*x*exp(1) +
10*x^3) + 4*x^5 - 4*x^6 + x^7), x)

________________________________________________________________________________________

sympy [B]  time = 0.39, size = 66, normalized size = 2.06 \begin {gather*} \frac {4 x^{3} - 20 e x - 8 x + \left (20 x + 40\right ) \log {\relax (x )} - 40 e - 16}{x^{3} - 2 x^{2} - 5 e x + \left (x^{2} + 3 x - 5 e\right ) \log {\relax (x )} + 5 \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((100*x*ln(x)**3+(-200*x*exp(1)+40*x**3-80*x**2-260*x-200)*ln(x)**2+(100*x*exp(1)**2+(-40*x**3+80*x**
2+560*x+400)*exp(1)+4*x**5-16*x**4-112*x**3+192*x**2+128*x+160)*ln(x)+(-300*x-200)*exp(1)**2+(120*x**3-160*x**
2-200*x-80)*exp(1)-12*x**5+24*x**4+40*x**3-104*x**2+48*x)/(25*x*ln(x)**4+(-50*x*exp(1)+10*x**3+30*x**2)*ln(x)*
*3+(25*x*exp(1)**2+(-10*x**3-80*x**2)*exp(1)+x**5+16*x**4-11*x**3)*ln(x)**2+(50*x**2*exp(1)**2+(-20*x**4-10*x*
*3)*exp(1)+2*x**6+2*x**5-12*x**4)*ln(x)+25*x**3*exp(1)**2+(-10*x**5+20*x**4)*exp(1)+x**7-4*x**6+4*x**5),x)

[Out]

(4*x**3 - 20*E*x - 8*x + (20*x + 40)*log(x) - 40*E - 16)/(x**3 - 2*x**2 - 5*E*x + (x**2 + 3*x - 5*E)*log(x) +
5*log(x)**2)

________________________________________________________________________________________