3.70.31 \(\int \frac {21600+76375 x-23350 x^2+(-15000-61000 x+19400 x^2) \log (x)+(3600+18500 x-6200 x^2) \log ^2(x)+(-300-2500 x+900 x^2) \log ^3(x)+(125 x-50 x^2) \log ^4(x)}{312987 x-558144 x \log (x)+442632 x \log ^2(x)-203808 x \log ^3(x)+59586 x \log ^4(x)-11328 x \log ^5(x)+1368 x \log ^6(x)-96 x \log ^7(x)+3 x \log ^8(x)} \, dx\)

Optimal. Leaf size=30 \[ \frac {25 \left (1+\frac {1}{3} (5-x) x\right )}{-1+\left (2+(4-\log (x))^2\right )^2} \]

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Rubi [F]  time = 4.18, 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 {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{312987 x-558144 x \log (x)+442632 x \log ^2(x)-203808 x \log ^3(x)+59586 x \log ^4(x)-11328 x \log ^5(x)+1368 x \log ^6(x)-96 x \log ^7(x)+3 x \log ^8(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(21600 + 76375*x - 23350*x^2 + (-15000 - 61000*x + 19400*x^2)*Log[x] + (3600 + 18500*x - 6200*x^2)*Log[x]^
2 + (-300 - 2500*x + 900*x^2)*Log[x]^3 + (125*x - 50*x^2)*Log[x]^4)/(312987*x - 558144*x*Log[x] + 442632*x*Log
[x]^2 - 203808*x*Log[x]^3 + 59586*x*Log[x]^4 - 11328*x*Log[x]^5 + 1368*x*Log[x]^6 - 96*x*Log[x]^7 + 3*x*Log[x]
^8),x]

[Out]

(125*E^(4 + I*Sqrt[3])*ExpIntegralEi[-4 - I*Sqrt[3] + Log[x]])/9 + (((125*I)/12)*E^(4 + I*Sqrt[3])*ExpIntegral
Ei[-4 - I*Sqrt[3] + Log[x]])/Sqrt[3] - (125*(4 + I*Sqrt[3])*E^(4 + I*Sqrt[3])*ExpIntegralEi[-4 - I*Sqrt[3] + L
og[x]])/36 + (125*E^(4 - I*Sqrt[3])*ExpIntegralEi[-4 + I*Sqrt[3] + Log[x]])/9 - (((125*I)/12)*E^(4 - I*Sqrt[3]
)*ExpIntegralEi[-4 + I*Sqrt[3] + Log[x]])/Sqrt[3] - (125*(4 - I*Sqrt[3])*E^(4 - I*Sqrt[3])*ExpIntegralEi[-4 +
I*Sqrt[3] + Log[x]])/36 + (((125*I)/6)*x)/((8 + 2*I) - 2*Log[x]) + (125*x)/(9*(4 - I*Sqrt[3] - Log[x])) - (125
*(4 - I*Sqrt[3])*x)/(36*(4 - I*Sqrt[3] - Log[x])) + (125*x)/(9*(4 + I*Sqrt[3] - Log[x])) - (125*(4 + I*Sqrt[3]
)*x)/(36*(4 + I*Sqrt[3] - Log[x])) + (((125*I)/6)*x)/((-8 + 2*I) + 2*Log[x]) + 25/(2*(17 - 8*Log[x] + Log[x]^2
)) - 25/(2*(19 - 8*Log[x] + Log[x]^2)) - (100*Defer[Int][x/(17 - 8*Log[x] + Log[x]^2)^2, x])/3 + (25*Defer[Int
][(x*Log[x])/(17 - 8*Log[x] + Log[x]^2)^2, x])/3 - (25*Defer[Int][x/(17 - 8*Log[x] + Log[x]^2), x])/3 + (100*D
efer[Int][x/(19 - 8*Log[x] + Log[x]^2)^2, x])/3 - (25*Defer[Int][(x*Log[x])/(19 - 8*Log[x] + Log[x]^2)^2, x])/
3 + (25*Defer[Int][x/(19 - 8*Log[x] + Log[x]^2), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{3 x \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{x \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {25 \left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2}-\frac {25 (-5+2 x)}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25 \left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {25 (-5+2 x)}{2 \left (19-8 \log (x)+\log ^2(x)\right )}\right ) \, dx\\ &=-\left (\frac {25}{6} \int \frac {-5+2 x}{17-8 \log (x)+\log ^2(x)} \, dx\right )+\frac {25}{6} \int \frac {-5+2 x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {25}{3} \int \frac {\left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {\left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=-\left (\frac {25}{6} \int \left (-\frac {5}{17-8 \log (x)+\log ^2(x)}+\frac {2 x}{17-8 \log (x)+\log ^2(x)}\right ) \, dx\right )+\frac {25}{6} \int \left (-\frac {5}{19-8 \log (x)+\log ^2(x)}+\frac {2 x}{19-8 \log (x)+\log ^2(x)}\right ) \, dx+\frac {25}{3} \int \left (-\frac {5 (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2}-\frac {3 (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {x (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx-\frac {25}{3} \int \left (-\frac {5 (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2}-\frac {3 (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {x (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=\frac {25}{3} \int \frac {x (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {125}{6} \int \frac {1}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {125}{6} \int \frac {1}{19-8 \log (x)+\log ^2(x)} \, dx-25 \int \frac {-4+\log (x)}{x \left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+25 \int \frac {-4+\log (x)}{x \left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \frac {-4+\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {125}{3} \int \frac {-4+\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=-\left (\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx\right )+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {25}{3} \int \left (-\frac {4 x}{\left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx-\frac {25}{3} \int \left (-\frac {4 x}{\left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx+\frac {125}{6} \int \left (\frac {i}{(8+2 i)-2 \log (x)}+\frac {i}{(-8+2 i)+2 \log (x)}\right ) \, dx-\frac {125}{6} \int \left (\frac {i}{\sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}+\frac {i}{\sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx-25 \operatorname {Subst}\left (\int \frac {-4+x}{\left (17-8 x+x^2\right )^2} \, dx,x,\log (x)\right )+25 \operatorname {Subst}\left (\int \frac {-4+x}{\left (19-8 x+x^2\right )^2} \, dx,x,\log (x)\right )-\frac {125}{3} \int \left (-\frac {4}{\left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx+\frac {125}{3} \int \left (-\frac {4}{\left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}+\frac {125}{6} i \int \frac {1}{(8+2 i)-2 \log (x)} \, dx+\frac {125}{6} i \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \frac {\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {125}{3} \int \frac {\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {500}{3} \int \frac {1}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {500}{3} \int \frac {1}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {(125 i) \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx}{6 \sqrt {3}}-\frac {(125 i) \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx}{6 \sqrt {3}}\\ &=\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}+\frac {125}{6} i \operatorname {Subst}\left (\int \frac {e^x}{(8+2 i)-2 x} \, dx,x,\log (x)\right )+\frac {125}{6} i \operatorname {Subst}\left (\int \frac {e^x}{(-8+2 i)+2 x} \, dx,x,\log (x)\right )+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \left (-\frac {4+i}{((8+2 i)-2 \log (x))^2}+\frac {2 i}{(8+2 i)-2 \log (x)}-\frac {4-i}{((-8+2 i)+2 \log (x))^2}+\frac {2 i}{(-8+2 i)+2 \log (x)}\right ) \, dx+\frac {125}{3} \int \left (-\frac {8+2 i \sqrt {3}}{6 \left (8+2 i \sqrt {3}-2 \log (x)\right )^2}+\frac {2 i}{3 \sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}-\frac {8-2 i \sqrt {3}}{6 \left (-8+2 i \sqrt {3}+2 \log (x)\right )^2}+\frac {2 i}{3 \sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx+\frac {500}{3} \int \left (-\frac {1}{((8+2 i)-2 \log (x))^2}+\frac {i}{2 ((8+2 i)-2 \log (x))}-\frac {1}{((-8+2 i)+2 \log (x))^2}+\frac {i}{2 ((-8+2 i)+2 \log (x))}\right ) \, dx-\frac {500}{3} \int \left (-\frac {1}{3 \left (8+2 i \sqrt {3}-2 \log (x)\right )^2}+\frac {i}{6 \sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}-\frac {1}{3 \left (-8+2 i \sqrt {3}+2 \log (x)\right )^2}+\frac {i}{6 \sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx-\frac {(125 i) \operatorname {Subst}\left (\int \frac {e^x}{8+2 i \sqrt {3}-2 x} \, dx,x,\log (x)\right )}{6 \sqrt {3}}-\frac {(125 i) \operatorname {Subst}\left (\int \frac {e^x}{-8+2 i \sqrt {3}+2 x} \, dx,x,\log (x)\right )}{6 \sqrt {3}}\\ &=\frac {125 i e^{4+i \sqrt {3}} \text {Ei}\left (-4-i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125 i e^{4-i \sqrt {3}} \text {Ei}\left (-4+i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125}{12} i e^{4+i} \text {Ei}\left (\frac {1}{2} ((-8-2 i)+2 \log (x))\right )+\frac {125}{12} i e^{4-i} \text {Ei}\left (\frac {1}{2} ((-8+2 i)+2 \log (x))\right )+\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}-\left (-\frac {500}{3}-\frac {125 i}{3}\right ) \int \frac {1}{((8+2 i)-2 \log (x))^2} \, dx-\left (-\frac {500}{3}+\frac {125 i}{3}\right ) \int \frac {1}{((-8+2 i)+2 \log (x))^2} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {500}{9} \int \frac {1}{\left (8+2 i \sqrt {3}-2 \log (x)\right )^2} \, dx+\frac {500}{9} \int \frac {1}{\left (-8+2 i \sqrt {3}+2 \log (x)\right )^2} \, dx-\frac {500}{3} \int \frac {1}{((8+2 i)-2 \log (x))^2} \, dx-\frac {500}{3} \int \frac {1}{((-8+2 i)+2 \log (x))^2} \, dx-\frac {1}{9} \left (125 \left (4-i \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 i \sqrt {3}+2 \log (x)\right )^2} \, dx-\frac {1}{9} \left (125 \left (4+i \sqrt {3}\right )\right ) \int \frac {1}{\left (8+2 i \sqrt {3}-2 \log (x)\right )^2} \, dx\\ &=\frac {125 i e^{4+i \sqrt {3}} \text {Ei}\left (-4-i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125 i e^{4-i \sqrt {3}} \text {Ei}\left (-4+i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125}{12} i e^{4+i} \text {Ei}\left (\frac {1}{2} ((-8-2 i)+2 \log (x))\right )+\frac {125}{12} i e^{4-i} \text {Ei}\left (\frac {1}{2} ((-8+2 i)+2 \log (x))\right )+\frac {125 i x}{6 ((8+2 i)-2 \log (x))}+\frac {125 x}{9 \left (4-i \sqrt {3}-\log (x)\right )}-\frac {125 \left (4-i \sqrt {3}\right ) x}{36 \left (4-i \sqrt {3}-\log (x)\right )}+\frac {125 x}{9 \left (4+i \sqrt {3}-\log (x)\right )}-\frac {125 \left (4+i \sqrt {3}\right ) x}{36 \left (4+i \sqrt {3}-\log (x)\right )}+\frac {125 i x}{6 ((-8+2 i)+2 \log (x))}+\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}-\left (-\frac {250}{3}+\frac {125 i}{6}\right ) \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {250}{9} \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx+\frac {250}{9} \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {250}{3} \int \frac {1}{(8+2 i)-2 \log (x)} \, dx-\frac {250}{3} \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx-\left (\frac {250}{3}+\frac {125 i}{6}\right ) \int \frac {1}{(8+2 i)-2 \log (x)} \, dx-\frac {1}{18} \left (125 \left (4-i \sqrt {3}\right )\right ) \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx+\frac {1}{18} \left (125 \left (4+i \sqrt {3}\right )\right ) \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 36, normalized size = 1.20 \begin {gather*} -\frac {25 \left (-3-5 x+x^2\right )}{3 \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(21600 + 76375*x - 23350*x^2 + (-15000 - 61000*x + 19400*x^2)*Log[x] + (3600 + 18500*x - 6200*x^2)*L
og[x]^2 + (-300 - 2500*x + 900*x^2)*Log[x]^3 + (125*x - 50*x^2)*Log[x]^4)/(312987*x - 558144*x*Log[x] + 442632
*x*Log[x]^2 - 203808*x*Log[x]^3 + 59586*x*Log[x]^4 - 11328*x*Log[x]^5 + 1368*x*Log[x]^6 - 96*x*Log[x]^7 + 3*x*
Log[x]^8),x]

[Out]

(-25*(-3 - 5*x + x^2))/(3*(323 - 288*Log[x] + 100*Log[x]^2 - 16*Log[x]^3 + Log[x]^4))

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fricas [A]  time = 0.52, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-50*x^2+125*x)*log(x)^4+(900*x^2-2500*x-300)*log(x)^3+(-6200*x^2+18500*x+3600)*log(x)^2+(19400*x^2
-61000*x-15000)*log(x)-23350*x^2+76375*x+21600)/(3*x*log(x)^8-96*x*log(x)^7+1368*x*log(x)^6-11328*x*log(x)^5+5
9586*x*log(x)^4-203808*x*log(x)^3+442632*x*log(x)^2-558144*x*log(x)+312987*x),x, algorithm="fricas")

[Out]

-25/3*(x^2 - 5*x - 3)/(log(x)^4 - 16*log(x)^3 + 100*log(x)^2 - 288*log(x) + 323)

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giac [A]  time = 0.18, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-50*x^2+125*x)*log(x)^4+(900*x^2-2500*x-300)*log(x)^3+(-6200*x^2+18500*x+3600)*log(x)^2+(19400*x^2
-61000*x-15000)*log(x)-23350*x^2+76375*x+21600)/(3*x*log(x)^8-96*x*log(x)^7+1368*x*log(x)^6-11328*x*log(x)^5+5
9586*x*log(x)^4-203808*x*log(x)^3+442632*x*log(x)^2-558144*x*log(x)+312987*x),x, algorithm="giac")

[Out]

-25/3*(x^2 - 5*x - 3)/(log(x)^4 - 16*log(x)^3 + 100*log(x)^2 - 288*log(x) + 323)

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maple [A]  time = 0.02, size = 35, normalized size = 1.17

method	result	size
risch	\(-\frac {25 \left (x^{2}-5 x -3\right )}{3 \left (\ln \relax (x )^{4}-16 \ln \relax (x )^{3}+100 \ln \relax (x )^{2}-288 \ln \relax (x )+323\right )}\)	\(35\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-50*x^2+125*x)*ln(x)^4+(900*x^2-2500*x-300)*ln(x)^3+(-6200*x^2+18500*x+3600)*ln(x)^2+(19400*x^2-61000*x-
15000)*ln(x)-23350*x^2+76375*x+21600)/(3*x*ln(x)^8-96*x*ln(x)^7+1368*x*ln(x)^6-11328*x*ln(x)^5+59586*x*ln(x)^4
-203808*x*ln(x)^3+442632*x*ln(x)^2-558144*x*ln(x)+312987*x),x,method=_RETURNVERBOSE)

[Out]

-25/3*(x^2-5*x-3)/(ln(x)^4-16*ln(x)^3+100*ln(x)^2-288*ln(x)+323)

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maxima [A]  time = 0.42, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-50*x^2+125*x)*log(x)^4+(900*x^2-2500*x-300)*log(x)^3+(-6200*x^2+18500*x+3600)*log(x)^2+(19400*x^2
-61000*x-15000)*log(x)-23350*x^2+76375*x+21600)/(3*x*log(x)^8-96*x*log(x)^7+1368*x*log(x)^6-11328*x*log(x)^5+5
9586*x*log(x)^4-203808*x*log(x)^3+442632*x*log(x)^2-558144*x*log(x)+312987*x),x, algorithm="maxima")

[Out]

-25/3*(x^2 - 5*x - 3)/(log(x)^4 - 16*log(x)^3 + 100*log(x)^2 - 288*log(x) + 323)

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mupad [B]  time = 4.41, size = 48, normalized size = 1.60 \begin {gather*} \frac {-\frac {25\,x^2}{6}+\frac {125\,x}{6}+\frac {25}{2}}{{\ln \relax (x)}^2-8\,\ln \relax (x)+17}-\frac {-\frac {25\,x^2}{6}+\frac {125\,x}{6}+\frac {25}{2}}{{\ln \relax (x)}^2-8\,\ln \relax (x)+19} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((76375*x + log(x)^4*(125*x - 50*x^2) - log(x)^3*(2500*x - 900*x^2 + 300) + log(x)^2*(18500*x - 6200*x^2 +
3600) - log(x)*(61000*x - 19400*x^2 + 15000) - 23350*x^2 + 21600)/(312987*x + 442632*x*log(x)^2 - 203808*x*log
(x)^3 + 59586*x*log(x)^4 - 11328*x*log(x)^5 + 1368*x*log(x)^6 - 96*x*log(x)^7 + 3*x*log(x)^8 - 558144*x*log(x)
),x)

[Out]

((125*x)/6 - (25*x^2)/6 + 25/2)/(log(x)^2 - 8*log(x) + 17) - ((125*x)/6 - (25*x^2)/6 + 25/2)/(log(x)^2 - 8*log
(x) + 19)

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sympy [A]  time = 0.18, size = 36, normalized size = 1.20 \begin {gather*} \frac {- 25 x^{2} + 125 x + 75}{3 \log {\relax (x )}^{4} - 48 \log {\relax (x )}^{3} + 300 \log {\relax (x )}^{2} - 864 \log {\relax (x )} + 969} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-50*x**2+125*x)*ln(x)**4+(900*x**2-2500*x-300)*ln(x)**3+(-6200*x**2+18500*x+3600)*ln(x)**2+(19400*
x**2-61000*x-15000)*ln(x)-23350*x**2+76375*x+21600)/(3*x*ln(x)**8-96*x*ln(x)**7+1368*x*ln(x)**6-11328*x*ln(x)*
*5+59586*x*ln(x)**4-203808*x*ln(x)**3+442632*x*ln(x)**2-558144*x*ln(x)+312987*x),x)

[Out]

(-25*x**2 + 125*x + 75)/(3*log(x)**4 - 48*log(x)**3 + 300*log(x)**2 - 864*log(x) + 969)

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