3.35.31 \(\int \frac {(-36 x^2+36 x \log (x)) \log (x-\log (x))+\frac {e^x (-15+15 x+(-15 x-15 x^2+(15+15 x) \log (x)) \log (x-\log (x)))}{\log (x-\log (x))}}{e^x (15 x^2-60 x^4+(-15 x+60 x^3) \log (x))+\frac {e^{2 x} (-25 x^3+25 x^2 \log (x))}{\log (x-\log (x))}+(18 x^3-36 x^5+(-18 x^2+36 x^4) \log (x)) \log (x-\log (x))} \, dx\)

Optimal. Leaf size=29 \[ \log \left (5-\frac {3}{x \left (\frac {6 x}{5}+\frac {e^x}{\log (x-\log (x))}\right )}\right ) \]

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Rubi [F]  time = 13.91, 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 {\left (-36 x^2+36 x \log (x)\right ) \log (x-\log (x))+\frac {e^x \left (-15+15 x+\left (-15 x-15 x^2+(15+15 x) \log (x)\right ) \log (x-\log (x))\right )}{\log (x-\log (x))}}{e^x \left (15 x^2-60 x^4+\left (-15 x+60 x^3\right ) \log (x)\right )+\frac {e^{2 x} \left (-25 x^3+25 x^2 \log (x)\right )}{\log (x-\log (x))}+\left (18 x^3-36 x^5+\left (-18 x^2+36 x^4\right ) \log (x)\right ) \log (x-\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-36*x^2 + 36*x*Log[x])*Log[x - Log[x]] + (E^x*(-15 + 15*x + (-15*x - 15*x^2 + (15 + 15*x)*Log[x])*Log[x
- Log[x]]))/Log[x - Log[x]])/(E^x*(15*x^2 - 60*x^4 + (-15*x + 60*x^3)*Log[x]) + (E^(2*x)*(-25*x^3 + 25*x^2*Log
[x]))/Log[x - Log[x]] + (18*x^3 - 36*x^5 + (-18*x^2 + 36*x^4)*Log[x])*Log[x - Log[x]]),x]

[Out]

6*Defer[Int][1/((x - Log[x])*(5*E^x + 6*x*Log[x - Log[x]])), x] - 6*Defer[Int][x/((x - Log[x])*(5*E^x + 6*x*Lo
g[x - Log[x]])), x] - 6*Defer[Int][(x*Log[x - Log[x]])/((x - Log[x])*(5*E^x + 6*x*Log[x - Log[x]])), x] + 6*De
fer[Int][(x^2*Log[x - Log[x]])/((x - Log[x])*(5*E^x + 6*x*Log[x - Log[x]])), x] + 6*Defer[Int][(Log[x]*Log[x -
Log[x]])/((x - Log[x])*(5*E^x + 6*x*Log[x - Log[x]])), x] - 6*Defer[Int][(x*Log[x]*Log[x - Log[x]])/((x - Log
[x])*(5*E^x + 6*x*Log[x - Log[x]])), x] - 3*Defer[Int][1/((x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Lo
g[x - Log[x]])), x] + 3*Defer[Int][1/(x*(x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x
] - 6*Defer[Int][x/((x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] + 6*Defer[Int][x^2
/((x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] + 3*Defer[Int][Log[x - Log[x]]/((x -
Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] + 3*Defer[Int][(x*Log[x - Log[x]])/((x - L
og[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] + 6*Defer[Int][(x^2*Log[x - Log[x]])/((x - L
og[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] - 6*Defer[Int][(x^3*Log[x - Log[x]])/((x - L
og[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] - 3*Defer[Int][(Log[x]*Log[x - Log[x]])/((x
- Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] - 3*Defer[Int][(Log[x]*Log[x - Log[x]])/(
x*(x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] - 6*Defer[Int][(x*Log[x]*Log[x - Log
[x]])/((x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x] + 6*Defer[Int][(x^2*Log[x]*Log[
x - Log[x]])/((x - Log[x])*(5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-5 e^x (-1+x)+5 e^x (1+x) (x-\log (x)) \log (x-\log (x))+12 x (x-\log (x)) \log ^2(x-\log (x))\right )}{x (x-\log (x)) \left (25 e^{2 x} x+15 e^x \left (-1+4 x^2\right ) \log (x-\log (x))+18 x \left (-1+2 x^2\right ) \log ^2(x-\log (x))\right )} \, dx\\ &=3 \int \frac {-5 e^x (-1+x)+5 e^x (1+x) (x-\log (x)) \log (x-\log (x))+12 x (x-\log (x)) \log ^2(x-\log (x))}{x (x-\log (x)) \left (25 e^{2 x} x+15 e^x \left (-1+4 x^2\right ) \log (x-\log (x))+18 x \left (-1+2 x^2\right ) \log ^2(x-\log (x))\right )} \, dx\\ &=3 \int \left (\frac {2 (-1+x) (-1+x \log (x-\log (x))-\log (x) \log (x-\log (x)))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}-\frac {-1+x+2 x^2-2 x^3-x \log (x-\log (x))-x^2 \log (x-\log (x))-2 x^3 \log (x-\log (x))+2 x^4 \log (x-\log (x))+\log (x) \log (x-\log (x))+x \log (x) \log (x-\log (x))+2 x^2 \log (x) \log (x-\log (x))-2 x^3 \log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}\right ) \, dx\\ &=-\left (3 \int \frac {-1+x+2 x^2-2 x^3-x \log (x-\log (x))-x^2 \log (x-\log (x))-2 x^3 \log (x-\log (x))+2 x^4 \log (x-\log (x))+\log (x) \log (x-\log (x))+x \log (x) \log (x-\log (x))+2 x^2 \log (x) \log (x-\log (x))-2 x^3 \log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx\right )+6 \int \frac {(-1+x) (-1+x \log (x-\log (x))-\log (x) \log (x-\log (x)))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx\\ &=-\left (3 \int \frac {-1+x+2 x^2-2 x^3+\left (-1-x-2 x^2+2 x^3\right ) (x-\log (x)) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x+\left (-3+6 x^2\right ) \log (x-\log (x))\right )} \, dx\right )+6 \int \left (-\frac {-1+x \log (x-\log (x))-\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}+\frac {x (-1+x \log (x-\log (x))-\log (x) \log (x-\log (x)))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}\right ) \, dx\\ &=-\left (3 \int \left (\frac {1}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {1}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}+\frac {2 x}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {2 x^2}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {\log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {2 x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}+\frac {2 x^3 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}+\frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}+\frac {\log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}+\frac {2 x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}-\frac {2 x^2 \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )}\right ) \, dx\right )-6 \int \frac {-1+x \log (x-\log (x))-\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx+6 \int \frac {x (-1+x \log (x-\log (x))-\log (x) \log (x-\log (x)))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx\\ &=-\left (3 \int \frac {1}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx\right )+3 \int \frac {1}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {\log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x^3 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {-1+(x-\log (x)) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx+6 \int \frac {x (-1+(x-\log (x)) \log (x-\log (x)))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx\\ &=-\left (3 \int \frac {1}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx\right )+3 \int \frac {1}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {\log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x^3 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \left (-\frac {1}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}+\frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}-\frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}\right ) \, dx+6 \int \left (-\frac {x}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}+\frac {x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}-\frac {x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )}\right ) \, dx\\ &=-\left (3 \int \frac {1}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx\right )+3 \int \frac {1}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {\log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+3 \int \frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-3 \int \frac {\log (x) \log (x-\log (x))}{x (x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {1}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx-6 \int \frac {x}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx-6 \int \frac {x \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx+6 \int \frac {\log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx-6 \int \frac {x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x+6 x \log (x-\log (x))\right )} \, dx-6 \int \frac {x}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x^3 \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx-6 \int \frac {x \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx+6 \int \frac {x^2 \log (x) \log (x-\log (x))}{(x-\log (x)) \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.56, size = 63, normalized size = 2.17 \begin {gather*} 3 \left (-\frac {\log (x)}{3}-\frac {1}{3} \log \left (5 e^x+6 x \log (x-\log (x))\right )+\frac {1}{3} \log \left (5 e^x x-3 \log (x-\log (x))+6 x^2 \log (x-\log (x))\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-36*x^2 + 36*x*Log[x])*Log[x - Log[x]] + (E^x*(-15 + 15*x + (-15*x - 15*x^2 + (15 + 15*x)*Log[x])*
Log[x - Log[x]]))/Log[x - Log[x]])/(E^x*(15*x^2 - 60*x^4 + (-15*x + 60*x^3)*Log[x]) + (E^(2*x)*(-25*x^3 + 25*x
^2*Log[x]))/Log[x - Log[x]] + (18*x^3 - 36*x^5 + (-18*x^2 + 36*x^4)*Log[x])*Log[x - Log[x]]),x]

[Out]

3*(-1/3*Log[x] - Log[5*E^x + 6*x*Log[x - Log[x]]]/3 + Log[5*E^x*x - 3*Log[x - Log[x]] + 6*x^2*Log[x - Log[x]]]
/3)

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fricas [A]  time = 0.96, size = 51, normalized size = 1.76 \begin {gather*} -\log \left (6 \, x + 5 \, e^{\left (x - \log \left (\log \left (x - \log \relax (x)\right )\right )\right )}\right ) + \log \left (\frac {6 \, x^{2} + 5 \, x e^{\left (x - \log \left (\log \left (x - \log \relax (x)\right )\right )\right )} - 3}{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((15*x+15)*log(x)-15*x^2-15*x)*log(x-log(x))+15*x-15)*exp(-log(log(x-log(x)))+x)+(36*x*log(x)-36*x
^2)*log(x-log(x)))/((25*x^2*log(x)-25*x^3)*log(x-log(x))*exp(-log(log(x-log(x)))+x)^2+((60*x^3-15*x)*log(x)-60
*x^4+15*x^2)*log(x-log(x))*exp(-log(log(x-log(x)))+x)+((36*x^4-18*x^2)*log(x)-36*x^5+18*x^3)*log(x-log(x))),x,
algorithm="fricas")

[Out]

-log(6*x + 5*e^(x - log(log(x - log(x))))) + log((6*x^2 + 5*x*e^(x - log(log(x - log(x)))) - 3)/x)

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giac [A]  time = 0.62, size = 51, normalized size = 1.76 \begin {gather*} \log \left (6 \, x^{2} \log \left (x - \log \relax (x)\right ) + 5 \, x e^{x} - 3 \, \log \left (x - \log \relax (x)\right )\right ) - \log \left (6 \, x \log \left (x - \log \relax (x)\right ) + 5 \, e^{x}\right ) - \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((15*x+15)*log(x)-15*x^2-15*x)*log(x-log(x))+15*x-15)*exp(-log(log(x-log(x)))+x)+(36*x*log(x)-36*x
^2)*log(x-log(x)))/((25*x^2*log(x)-25*x^3)*log(x-log(x))*exp(-log(log(x-log(x)))+x)^2+((60*x^3-15*x)*log(x)-60
*x^4+15*x^2)*log(x-log(x))*exp(-log(log(x-log(x)))+x)+((36*x^4-18*x^2)*log(x)-36*x^5+18*x^3)*log(x-log(x))),x,
algorithm="giac")

[Out]

log(6*x^2*log(x - log(x)) + 5*x*e^x - 3*log(x - log(x))) - log(6*x*log(x - log(x)) + 5*e^x) - log(x)

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maple [A]  time = 0.05, size = 47, normalized size = 1.62

method	result	size
risch	\(\ln \left (\frac {{\mathrm e}^{x}}{\ln \left (x -\ln \relax (x )\right )}+\frac {\frac {6 x^{2}}{5}-\frac {3}{5}}{x}\right )-\ln \left (\frac {{\mathrm e}^{x}}{\ln \left (x -\ln \relax (x )\right )}+\frac {6 x}{5}\right )\)	\(47\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((15*x+15)*ln(x)-15*x^2-15*x)*ln(x-ln(x))+15*x-15)*exp(-ln(ln(x-ln(x)))+x)+(36*x*ln(x)-36*x^2)*ln(x-ln(x
)))/((25*x^2*ln(x)-25*x^3)*ln(x-ln(x))*exp(-ln(ln(x-ln(x)))+x)^2+((60*x^3-15*x)*ln(x)-60*x^4+15*x^2)*ln(x-ln(x
))*exp(-ln(ln(x-ln(x)))+x)+((36*x^4-18*x^2)*ln(x)-36*x^5+18*x^3)*ln(x-ln(x))),x,method=_RETURNVERBOSE)

[Out]

ln(1/ln(x-ln(x))*exp(x)+3/5*(2*x^2-1)/x)-ln(1/ln(x-ln(x))*exp(x)+6/5*x)

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maxima [B]  time = 0.63, size = 70, normalized size = 2.41 \begin {gather*} \log \left (2 \, x^{2} - 1\right ) - 2 \, \log \relax (x) + \log \left (\frac {5 \, x e^{x} + 3 \, {\left (2 \, x^{2} - 1\right )} \log \left (x - \log \relax (x)\right )}{3 \, {\left (2 \, x^{2} - 1\right )}}\right ) - \log \left (\frac {6 \, x \log \left (x - \log \relax (x)\right ) + 5 \, e^{x}}{6 \, x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((15*x+15)*log(x)-15*x^2-15*x)*log(x-log(x))+15*x-15)*exp(-log(log(x-log(x)))+x)+(36*x*log(x)-36*x
^2)*log(x-log(x)))/((25*x^2*log(x)-25*x^3)*log(x-log(x))*exp(-log(log(x-log(x)))+x)^2+((60*x^3-15*x)*log(x)-60
*x^4+15*x^2)*log(x-log(x))*exp(-log(log(x-log(x)))+x)+((36*x^4-18*x^2)*log(x)-36*x^5+18*x^3)*log(x-log(x))),x,
algorithm="maxima")

[Out]

log(2*x^2 - 1) - 2*log(x) + log(1/3*(5*x*e^x + 3*(2*x^2 - 1)*log(x - log(x)))/(2*x^2 - 1)) - log(1/6*(6*x*log(
x - log(x)) + 5*e^x)/x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {\ln \left (x-\ln \relax (x)\right )\,\left (36\,x\,\ln \relax (x)-36\,x^2\right )-{\mathrm {e}}^{x-\ln \left (\ln \left (x-\ln \relax (x)\right )\right )}\,\left (\ln \left (x-\ln \relax (x)\right )\,\left (15\,x-\ln \relax (x)\,\left (15\,x+15\right )+15\,x^2\right )-15\,x+15\right )}{\ln \left (x-\ln \relax (x)\right )\,\left (\ln \relax (x)\,\left (18\,x^2-36\,x^4\right )-18\,x^3+36\,x^5\right )-{\mathrm {e}}^{2\,x-2\,\ln \left (\ln \left (x-\ln \relax (x)\right )\right )}\,\ln \left (x-\ln \relax (x)\right )\,\left (25\,x^2\,\ln \relax (x)-25\,x^3\right )+{\mathrm {e}}^{x-\ln \left (\ln \left (x-\ln \relax (x)\right )\right )}\,\ln \left (x-\ln \relax (x)\right )\,\left (\ln \relax (x)\,\left (15\,x-60\,x^3\right )-15\,x^2+60\,x^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x - log(x))*(36*x*log(x) - 36*x^2) - exp(x - log(log(x - log(x))))*(log(x - log(x))*(15*x - log(x)*(
15*x + 15) + 15*x^2) - 15*x + 15))/(log(x - log(x))*(log(x)*(18*x^2 - 36*x^4) - 18*x^3 + 36*x^5) - exp(2*x - 2
*log(log(x - log(x))))*log(x - log(x))*(25*x^2*log(x) - 25*x^3) + exp(x - log(log(x - log(x))))*log(x - log(x)
)*(log(x)*(15*x - 60*x^3) - 15*x^2 + 60*x^4)),x)

[Out]

-int((log(x - log(x))*(36*x*log(x) - 36*x^2) - exp(x - log(log(x - log(x))))*(log(x - log(x))*(15*x - log(x)*(
15*x + 15) + 15*x^2) - 15*x + 15))/(log(x - log(x))*(log(x)*(18*x^2 - 36*x^4) - 18*x^3 + 36*x^5) - exp(2*x - 2
*log(log(x - log(x))))*log(x - log(x))*(25*x^2*log(x) - 25*x^3) + exp(x - log(log(x - log(x))))*log(x - log(x)
)*(log(x)*(15*x - 60*x^3) - 15*x^2 + 60*x^4)), x)

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((15*x+15)*ln(x)-15*x**2-15*x)*ln(x-ln(x))+15*x-15)*exp(-ln(ln(x-ln(x)))+x)+(36*x*ln(x)-36*x**2)*l
n(x-ln(x)))/((25*x**2*ln(x)-25*x**3)*ln(x-ln(x))*exp(-ln(ln(x-ln(x)))+x)**2+((60*x**3-15*x)*ln(x)-60*x**4+15*x
**2)*ln(x-ln(x))*exp(-ln(ln(x-ln(x)))+x)+((36*x**4-18*x**2)*ln(x)-36*x**5+18*x**3)*ln(x-ln(x))),x)

[Out]

Exception raised: PolynomialError

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