3.23.8 \(\int \frac {-1912 x+81 x^2-x^3+e^5 (-7680+324 x-4 x^2)+(-479 x+10 x^2+e^5 (-1920+40 x)) \log (x)+(-120 e^5-30 x) \log ^2(x)+(-89 x+2 x^2+e^5 (-356+8 x)+(-44 e^5-11 x) \log (x)) \log (\frac {1}{4} (4 e^5+x))+(-4 e^5-x) \log ^2(\frac {1}{4} (4 e^5+x))}{1600 x-80 x^2+x^3+e^5 (6400-320 x+4 x^2)+(e^5 (1600-40 x)+400 x-10 x^2) \log (x)+(100 e^5+25 x) \log ^2(x)+(e^5 (320-8 x)+80 x-2 x^2+(40 e^5+10 x) \log (x)) \log (\frac {1}{4} (4 e^5+x))+(4 e^5+x) \log ^2(\frac {1}{4} (4 e^5+x))} \, dx\)

Optimal. Leaf size=33 \[ -x+\frac {x}{-5+\frac {-x+\log \left (e^5+\frac {x}{4}\right )}{-8-\log (x)}} \]

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Rubi [F]  time = 4.29, 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 {-1912 x+81 x^2-x^3+e^5 \left (-7680+324 x-4 x^2\right )+\left (-479 x+10 x^2+e^5 (-1920+40 x)\right ) \log (x)+\left (-120 e^5-30 x\right ) \log ^2(x)+\left (-89 x+2 x^2+e^5 (-356+8 x)+\left (-44 e^5-11 x\right ) \log (x)\right ) \log \left (\frac {1}{4} \left (4 e^5+x\right )\right )+\left (-4 e^5-x\right ) \log ^2\left (\frac {1}{4} \left (4 e^5+x\right )\right )}{1600 x-80 x^2+x^3+e^5 \left (6400-320 x+4 x^2\right )+\left (e^5 (1600-40 x)+400 x-10 x^2\right ) \log (x)+\left (100 e^5+25 x\right ) \log ^2(x)+\left (e^5 (320-8 x)+80 x-2 x^2+\left (40 e^5+10 x\right ) \log (x)\right ) \log \left (\frac {1}{4} \left (4 e^5+x\right )\right )+\left (4 e^5+x\right ) \log ^2\left (\frac {1}{4} \left (4 e^5+x\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1912*x + 81*x^2 - x^3 + E^5*(-7680 + 324*x - 4*x^2) + (-479*x + 10*x^2 + E^5*(-1920 + 40*x))*Log[x] + (-
120*E^5 - 30*x)*Log[x]^2 + (-89*x + 2*x^2 + E^5*(-356 + 8*x) + (-44*E^5 - 11*x)*Log[x])*Log[(4*E^5 + x)/4] + (
-4*E^5 - x)*Log[(4*E^5 + x)/4]^2)/(1600*x - 80*x^2 + x^3 + E^5*(6400 - 320*x + 4*x^2) + (E^5*(1600 - 40*x) + 4
00*x - 10*x^2)*Log[x] + (100*E^5 + 25*x)*Log[x]^2 + (E^5*(320 - 8*x) + 80*x - 2*x^2 + (40*E^5 + 10*x)*Log[x])*
Log[(4*E^5 + x)/4] + (4*E^5 + x)*Log[(4*E^5 + x)/4]^2),x]

[Out]

(-6*x)/5 - (4*E^5*Defer[Int][(-40 + x - Log[E^5 + x/4] - 5*Log[x])^(-2), x])/5 + (6*Defer[Int][x/(-40 + x - Lo
g[E^5 + x/4] - 5*Log[x])^2, x])/5 - Defer[Int][x^2/(-40 + x - Log[E^5 + x/4] - 5*Log[x])^2, x]/5 + (16*E^10*De
fer[Int][1/((4*E^5 + x)*(-40 + x - Log[E^5 + x/4] - 5*Log[x])^2), x])/5 + Defer[Int][(x*Log[E^5 + x/4])/(-40 +
x - Log[E^5 + x/4] - 5*Log[x])^2, x]/5 + (4*E^5*Defer[Int][Log[E^5 + x/4]/((4*E^5 + x)*(-40 + x - Log[E^5 + x
/4] - 5*Log[x])^2), x])/5 - (8*E^5*Defer[Int][(-40 + x - Log[E^5 + x/4] - 5*Log[x])^(-1), x])/5 - ((1 - 8*E^5)
*Defer[Int][(-40 + x - Log[E^5 + x/4] - 5*Log[x])^(-1), x])/5 + (2*Defer[Int][x/(-40 + x - Log[E^5 + x/4] - 5*
Log[x]), x])/5 + (32*E^10*Defer[Int][1/((4*E^5 + x)*(-40 + x - Log[E^5 + x/4] - 5*Log[x])), x])/5 + (4*E^5*(1
- 8*E^5)*Defer[Int][1/((4*E^5 + x)*(-40 + x - Log[E^5 + x/4] - 5*Log[x])), x])/5 - (6*Defer[Int][Log[E^5 + x/4
]/(40 - x + Log[E^5 + x/4] + 5*Log[x])^2, x])/5 + Defer[Int][Log[E^5 + x/4]/(40 - x + Log[E^5 + x/4] + 5*Log[x
]), x]/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-7680 e^5-1912 \left (1-\frac {81 e^5}{478}\right ) x+81 \left (1-\frac {4 e^5}{81}\right ) x^2-x^3-\left (4 e^5+x\right ) \log ^2\left (e^5+\frac {x}{4}\right )+\left (4 e^5+x\right ) \log \left (e^5+\frac {x}{4}\right ) (-89+2 x-11 \log (x))-\left (-40 e^5 (-48+x)+(479-10 x) x\right ) \log (x)-30 \left (4 e^5+x\right ) \log ^2(x)}{\left (4 e^5+x\right ) \left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2} \, dx\\ &=\int \left (-\frac {6}{5}+\frac {\left (20 e^5+2 \left (3-2 e^5\right ) x-x^2\right ) \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{5 \left (4 e^5+x\right ) \left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2}+\frac {\left (1-8 e^5\right ) x-2 x^2+4 e^5 \log \left (e^5+\frac {x}{4}\right )+x \log \left (e^5+\frac {x}{4}\right )}{5 \left (4 e^5+x\right ) \left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )}\right ) \, dx\\ &=-\frac {6 x}{5}+\frac {1}{5} \int \frac {\left (20 e^5+2 \left (3-2 e^5\right ) x-x^2\right ) \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{\left (4 e^5+x\right ) \left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {\left (1-8 e^5\right ) x-2 x^2+4 e^5 \log \left (e^5+\frac {x}{4}\right )+x \log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )} \, dx\\ &=-\frac {6 x}{5}+\frac {1}{5} \int \left (\frac {6 \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {x \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {4 e^5 \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}\right ) \, dx+\frac {1}{5} \int \left (\frac {\left (-1+8 e^5\right ) x}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}+\frac {2 x^2}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}-\frac {4 e^5 \log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}-\frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}\right ) \, dx\\ &=-\frac {6 x}{5}-\frac {1}{5} \int \frac {x \left (x-\log \left (e^5+\frac {x}{4}\right )\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \int \frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {2}{5} \int \frac {x^2}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {6}{5} \int \frac {x-\log \left (e^5+\frac {x}{4}\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (4 e^5\right ) \int \frac {x-\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (4 e^5\right ) \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (-1+8 e^5\right ) \int \frac {x}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx\\ &=-\frac {6 x}{5}-\frac {1}{5} \int \left (\frac {x^2}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}\right ) \, dx-\frac {1}{5} \int \left (-\frac {4 e^5 \log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}-\frac {\log \left (e^5+\frac {x}{4}\right )}{40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)}\right ) \, dx+\frac {2}{5} \int \left (-\frac {4 e^5}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)}+\frac {x}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)}+\frac {16 e^{10}}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}\right ) \, dx+\frac {6}{5} \int \left (\frac {x}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {\log \left (e^5+\frac {x}{4}\right )}{\left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2}\right ) \, dx-\frac {1}{5} \left (4 e^5\right ) \int \left (\frac {x}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}\right ) \, dx-\frac {1}{5} \left (4 e^5\right ) \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (-1+8 e^5\right ) \int \left (\frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)}-\frac {4 e^5}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )}\right ) \, dx\\ &=-\frac {6 x}{5}-\frac {1}{5} \int \frac {x^2}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)} \, dx+\frac {2}{5} \int \frac {x}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {6}{5} \int \frac {x}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {6}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (4 e^5\right ) \int \frac {x}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \left (4 e^5\right ) \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {1}{5} \left (32 e^{10}\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (4 e^5 \left (1-8 e^5\right )\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (-1+8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx\\ &=-\frac {6 x}{5}-\frac {1}{5} \int \frac {x^2}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)} \, dx+\frac {2}{5} \int \frac {x}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {6}{5} \int \frac {x}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {6}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (4 e^5\right ) \int \left (\frac {1}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}-\frac {4 e^5}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2}\right ) \, dx+\frac {1}{5} \left (4 e^5\right ) \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {1}{5} \left (32 e^{10}\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (4 e^5 \left (1-8 e^5\right )\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (-1+8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx\\ &=-\frac {6 x}{5}-\frac {1}{5} \int \frac {x^2}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {x \log \left (e^5+\frac {x}{4}\right )}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)} \, dx+\frac {2}{5} \int \frac {x}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {6}{5} \int \frac {x}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {6}{5} \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (4 e^5\right ) \int \frac {1}{\left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \left (4 e^5\right ) \int \frac {\log \left (e^5+\frac {x}{4}\right )}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx-\frac {1}{5} \left (8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx+\frac {1}{5} \left (16 e^{10}\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )^2} \, dx+\frac {1}{5} \left (32 e^{10}\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (4 e^5 \left (1-8 e^5\right )\right ) \int \frac {1}{\left (4 e^5+x\right ) \left (-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)\right )} \, dx+\frac {1}{5} \left (-1+8 e^5\right ) \int \frac {1}{-40+x-\log \left (e^5+\frac {x}{4}\right )-5 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 43, normalized size = 1.30 \begin {gather*} -\frac {1}{5} x \left (6+\frac {x-\log \left (e^5+\frac {x}{4}\right )}{40-x+\log \left (e^5+\frac {x}{4}\right )+5 \log (x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1912*x + 81*x^2 - x^3 + E^5*(-7680 + 324*x - 4*x^2) + (-479*x + 10*x^2 + E^5*(-1920 + 40*x))*Log[x
] + (-120*E^5 - 30*x)*Log[x]^2 + (-89*x + 2*x^2 + E^5*(-356 + 8*x) + (-44*E^5 - 11*x)*Log[x])*Log[(4*E^5 + x)/
4] + (-4*E^5 - x)*Log[(4*E^5 + x)/4]^2)/(1600*x - 80*x^2 + x^3 + E^5*(6400 - 320*x + 4*x^2) + (E^5*(1600 - 40*
x) + 400*x - 10*x^2)*Log[x] + (100*E^5 + 25*x)*Log[x]^2 + (E^5*(320 - 8*x) + 80*x - 2*x^2 + (40*E^5 + 10*x)*Lo
g[x])*Log[(4*E^5 + x)/4] + (4*E^5 + x)*Log[(4*E^5 + x)/4]^2),x]

[Out]

-1/5*(x*(6 + (x - Log[E^5 + x/4])/(40 - x + Log[E^5 + x/4] + 5*Log[x])))

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fricas [A]  time = 0.71, size = 42, normalized size = 1.27 \begin {gather*} -\frac {x^{2} - 6 \, x \log \relax (x) - x \log \left (\frac {1}{4} \, x + e^{5}\right ) - 48 \, x}{x - 5 \, \log \relax (x) - \log \left (\frac {1}{4} \, x + e^{5}\right ) - 40} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(5)-x)*log(exp(5)+1/4*x)^2+((-44*exp(5)-11*x)*log(x)+(8*x-356)*exp(5)+2*x^2-89*x)*log(exp(5)
+1/4*x)+(-120*exp(5)-30*x)*log(x)^2+((40*x-1920)*exp(5)+10*x^2-479*x)*log(x)+(-4*x^2+324*x-7680)*exp(5)-x^3+81
*x^2-1912*x)/((4*exp(5)+x)*log(exp(5)+1/4*x)^2+((40*exp(5)+10*x)*log(x)+(-8*x+320)*exp(5)-2*x^2+80*x)*log(exp(
5)+1/4*x)+(100*exp(5)+25*x)*log(x)^2+((-40*x+1600)*exp(5)-10*x^2+400*x)*log(x)+(4*x^2-320*x+6400)*exp(5)+x^3-8
0*x^2+1600*x),x, algorithm="fricas")

[Out]

-(x^2 - 6*x*log(x) - x*log(1/4*x + e^5) - 48*x)/(x - 5*log(x) - log(1/4*x + e^5) - 40)

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giac [A]  time = 0.41, size = 51, normalized size = 1.55 \begin {gather*} -\frac {x^{2} + 2 \, x \log \relax (2) - x \log \left (x + 4 \, e^{5}\right ) - 6 \, x \log \relax (x) - 48 \, x}{x + 2 \, \log \relax (2) - \log \left (x + 4 \, e^{5}\right ) - 5 \, \log \relax (x) - 40} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(5)-x)*log(exp(5)+1/4*x)^2+((-44*exp(5)-11*x)*log(x)+(8*x-356)*exp(5)+2*x^2-89*x)*log(exp(5)
+1/4*x)+(-120*exp(5)-30*x)*log(x)^2+((40*x-1920)*exp(5)+10*x^2-479*x)*log(x)+(-4*x^2+324*x-7680)*exp(5)-x^3+81
*x^2-1912*x)/((4*exp(5)+x)*log(exp(5)+1/4*x)^2+((40*exp(5)+10*x)*log(x)+(-8*x+320)*exp(5)-2*x^2+80*x)*log(exp(
5)+1/4*x)+(100*exp(5)+25*x)*log(x)^2+((-40*x+1600)*exp(5)-10*x^2+400*x)*log(x)+(4*x^2-320*x+6400)*exp(5)+x^3-8
0*x^2+1600*x),x, algorithm="giac")

[Out]

-(x^2 + 2*x*log(2) - x*log(x + 4*e^5) - 6*x*log(x) - 48*x)/(x + 2*log(2) - log(x + 4*e^5) - 5*log(x) - 40)

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maple [A]  time = 0.06, size = 29, normalized size = 0.88

method	result	size
risch	\(-x +\frac {\left (\ln \relax (x )+8\right ) x}{x -5 \ln \relax (x )-\ln \left ({\mathrm e}^{5}+\frac {x}{4}\right )-40}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*exp(5)-x)*ln(exp(5)+1/4*x)^2+((-44*exp(5)-11*x)*ln(x)+(8*x-356)*exp(5)+2*x^2-89*x)*ln(exp(5)+1/4*x)+(
-120*exp(5)-30*x)*ln(x)^2+((40*x-1920)*exp(5)+10*x^2-479*x)*ln(x)+(-4*x^2+324*x-7680)*exp(5)-x^3+81*x^2-1912*x
)/((4*exp(5)+x)*ln(exp(5)+1/4*x)^2+((40*exp(5)+10*x)*ln(x)+(-8*x+320)*exp(5)-2*x^2+80*x)*ln(exp(5)+1/4*x)+(100
*exp(5)+25*x)*ln(x)^2+((-40*x+1600)*exp(5)-10*x^2+400*x)*ln(x)+(4*x^2-320*x+6400)*exp(5)+x^3-80*x^2+1600*x),x,
method=_RETURNVERBOSE)

[Out]

-x+(ln(x)+8)*x/(x-5*ln(x)-ln(exp(5)+1/4*x)-40)

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maxima [A]  time = 0.57, size = 50, normalized size = 1.52 \begin {gather*} -\frac {x^{2} + 2 \, x {\left (\log \relax (2) - 24\right )} - x \log \left (x + 4 \, e^{5}\right ) - 6 \, x \log \relax (x)}{x + 2 \, \log \relax (2) - \log \left (x + 4 \, e^{5}\right ) - 5 \, \log \relax (x) - 40} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(5)-x)*log(exp(5)+1/4*x)^2+((-44*exp(5)-11*x)*log(x)+(8*x-356)*exp(5)+2*x^2-89*x)*log(exp(5)
+1/4*x)+(-120*exp(5)-30*x)*log(x)^2+((40*x-1920)*exp(5)+10*x^2-479*x)*log(x)+(-4*x^2+324*x-7680)*exp(5)-x^3+81
*x^2-1912*x)/((4*exp(5)+x)*log(exp(5)+1/4*x)^2+((40*exp(5)+10*x)*log(x)+(-8*x+320)*exp(5)-2*x^2+80*x)*log(exp(
5)+1/4*x)+(100*exp(5)+25*x)*log(x)^2+((-40*x+1600)*exp(5)-10*x^2+400*x)*log(x)+(4*x^2-320*x+6400)*exp(5)+x^3-8
0*x^2+1600*x),x, algorithm="maxima")

[Out]

-(x^2 + 2*x*(log(2) - 24) - x*log(x + 4*e^5) - 6*x*log(x))/(x + 2*log(2) - log(x + 4*e^5) - 5*log(x) - 40)

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mupad [B]  time = 2.44, size = 187, normalized size = 5.67 \begin {gather*} \ln \relax (x)-x+\frac {54\,x+180\,{\mathrm {e}}^5}{x^2+\left (4\,{\mathrm {e}}^5-6\right )\,x-20\,{\mathrm {e}}^5}+\frac {\frac {x\,\left (312\,x+1280\,{\mathrm {e}}^5+20\,{\mathrm {e}}^5\,{\ln \relax (x)}^2+5\,x\,{\ln \relax (x)}^2-4\,x\,{\mathrm {e}}^5+320\,{\mathrm {e}}^5\,\ln \relax (x)+79\,x\,\ln \relax (x)-x^2\right )}{6\,x+20\,{\mathrm {e}}^5-4\,x\,{\mathrm {e}}^5-x^2}+\frac {x\,\ln \left (\frac {x}{4}+{\mathrm {e}}^5\right )\,\left (\ln \relax (x)+9\right )\,\left (x+4\,{\mathrm {e}}^5\right )}{6\,x+20\,{\mathrm {e}}^5-4\,x\,{\mathrm {e}}^5-x^2}}{\ln \left (\frac {x}{4}+{\mathrm {e}}^5\right )-x+5\,\ln \relax (x)+40}+\frac {\ln \relax (x)\,\left (6\,x+20\,{\mathrm {e}}^5\right )}{x^2+\left (4\,{\mathrm {e}}^5-6\right )\,x-20\,{\mathrm {e}}^5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(1912*x + log(x/4 + exp(5))*(89*x + log(x)*(11*x + 44*exp(5)) - 2*x^2 - exp(5)*(8*x - 356)) + exp(5)*(4*x
^2 - 324*x + 7680) + log(x/4 + exp(5))^2*(x + 4*exp(5)) + log(x)^2*(30*x + 120*exp(5)) - log(x)*(10*x^2 - 479*
x + exp(5)*(40*x - 1920)) - 81*x^2 + x^3)/(1600*x + log(x/4 + exp(5))*(80*x + log(x)*(10*x + 40*exp(5)) - 2*x^
2 - exp(5)*(8*x - 320)) + exp(5)*(4*x^2 - 320*x + 6400) + log(x/4 + exp(5))^2*(x + 4*exp(5)) + log(x)^2*(25*x
+ 100*exp(5)) - log(x)*(10*x^2 - 400*x + exp(5)*(40*x - 1600)) - 80*x^2 + x^3),x)

[Out]

log(x) - x + (54*x + 180*exp(5))/(x^2 - 20*exp(5) + x*(4*exp(5) - 6)) + ((x*(312*x + 1280*exp(5) + 20*exp(5)*l
og(x)^2 + 5*x*log(x)^2 - 4*x*exp(5) + 320*exp(5)*log(x) + 79*x*log(x) - x^2))/(6*x + 20*exp(5) - 4*x*exp(5) -
x^2) + (x*log(x/4 + exp(5))*(log(x) + 9)*(x + 4*exp(5)))/(6*x + 20*exp(5) - 4*x*exp(5) - x^2))/(log(x/4 + exp(
5)) - x + 5*log(x) + 40) + (log(x)*(6*x + 20*exp(5)))/(x^2 - 20*exp(5) + x*(4*exp(5) - 6))

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sympy [A]  time = 0.41, size = 27, normalized size = 0.82 \begin {gather*} - x + \frac {- x \log {\relax (x )} - 8 x}{- x + 5 \log {\relax (x )} + \log {\left (\frac {x}{4} + e^{5} \right )} + 40} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*exp(5)-x)*ln(exp(5)+1/4*x)**2+((-44*exp(5)-11*x)*ln(x)+(8*x-356)*exp(5)+2*x**2-89*x)*ln(exp(5)+
1/4*x)+(-120*exp(5)-30*x)*ln(x)**2+((40*x-1920)*exp(5)+10*x**2-479*x)*ln(x)+(-4*x**2+324*x-7680)*exp(5)-x**3+8
1*x**2-1912*x)/((4*exp(5)+x)*ln(exp(5)+1/4*x)**2+((40*exp(5)+10*x)*ln(x)+(-8*x+320)*exp(5)-2*x**2+80*x)*ln(exp
(5)+1/4*x)+(100*exp(5)+25*x)*ln(x)**2+((-40*x+1600)*exp(5)-10*x**2+400*x)*ln(x)+(4*x**2-320*x+6400)*exp(5)+x**
3-80*x**2+1600*x),x)

[Out]

-x + (-x*log(x) - 8*x)/(-x + 5*log(x) + log(x/4 + exp(5)) + 40)

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