3.54.70 \(\int \frac {90 x-114 x^2+46 x^3-6 x^4+e^{\frac {-6+x}{-6+2 x}} (21 x-21 x^2+4 x^3) \log (2)+(198 x-186 x^2+58 x^3-6 x^4) \log (2)+(90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} (-90+78 x-22 x^2+2 x^3) \log (2)+(-270+324 x-144 x^2+28 x^3-2 x^4) \log (2)) \log (\frac {-25 x+10 x^2-x^3+e^{\frac {-6+x}{-6+2 x}} (25-10 x+x^2) \log (2)+(75-55 x+13 x^2-x^3) \log (2)}{\log (2)})}{90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} (-90+78 x-22 x^2+2 x^3) \log (2)+(-270+324 x-144 x^2+28 x^3-2 x^4) \log (2)} \, dx\)

Optimal. Leaf size=39 \[ x \log \left ((5-x)^2 \left (3+e^{\frac {1}{2} \left (2-\frac {x}{-3+x}\right )}-x-\frac {x}{\log (2)}\right )\right ) \]

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Rubi [F]  time = 75.54, 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 {90 x-114 x^2+46 x^3-6 x^4+e^{\frac {-6+x}{-6+2 x}} \left (21 x-21 x^2+4 x^3\right ) \log (2)+\left (198 x-186 x^2+58 x^3-6 x^4\right ) \log (2)+\left (90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} \left (-90+78 x-22 x^2+2 x^3\right ) \log (2)+\left (-270+324 x-144 x^2+28 x^3-2 x^4\right ) \log (2)\right ) \log \left (\frac {-25 x+10 x^2-x^3+e^{\frac {-6+x}{-6+2 x}} \left (25-10 x+x^2\right ) \log (2)+\left (75-55 x+13 x^2-x^3\right ) \log (2)}{\log (2)}\right )}{90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} \left (-90+78 x-22 x^2+2 x^3\right ) \log (2)+\left (-270+324 x-144 x^2+28 x^3-2 x^4\right ) \log (2)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(90*x - 114*x^2 + 46*x^3 - 6*x^4 + E^((-6 + x)/(-6 + 2*x))*(21*x - 21*x^2 + 4*x^3)*Log[2] + (198*x - 186*x
^2 + 58*x^3 - 6*x^4)*Log[2] + (90*x - 78*x^2 + 22*x^3 - 2*x^4 + E^((-6 + x)/(-6 + 2*x))*(-90 + 78*x - 22*x^2 +
2*x^3)*Log[2] + (-270 + 324*x - 144*x^2 + 28*x^3 - 2*x^4)*Log[2])*Log[(-25*x + 10*x^2 - x^3 + E^((-6 + x)/(-6
+ 2*x))*(25 - 10*x + x^2)*Log[2] + (75 - 55*x + 13*x^2 - x^3)*Log[2])/Log[2]])/(90*x - 78*x^2 + 22*x^3 - 2*x^
4 + E^((-6 + x)/(-6 + 2*x))*(-90 + 78*x - 22*x^2 + 2*x^3)*Log[2] + (-270 + 324*x - 144*x^2 + 28*x^3 - 2*x^4)*L
og[2]),x]

[Out]

x*Log[(5 - x)^2*(E^((6 - x)/(2*(3 - x))) - (x*(1 + Log[2]) - Log[8])/Log[2])] - (3*(1 + Log[2])*Log[4]*Defer[I
nt][E^(3/(-3 + x))/(-(E^(x/(-6 + 2*x))*Log[2]) + E^(3/(-3 + x))*x*(1 + Log[2]) - E^(3/(-3 + x))*Log[8]), x])/L
og[16] - ((3 + Log[8])*Defer[Int][E^(3/(-3 + x))/(E^(x/(2*(-3 + x)))*Log[2] - E^(3/(-3 + x))*x*(1 + Log[2]) +
E^(3/(-3 + x))*Log[8]), x])/2 - (27*Defer[Int][E^(3/(-3 + x))/((3 - x)^2*(E^(x/(2*(-3 + x)))*Log[2] - E^(3/(-3
+ x))*x*(1 + Log[2]) + E^(3/(-3 + x))*Log[8])), x])/2 + ((2 + Log[4])*Defer[Int][(E^(3/(-3 + x))*x)/(E^(x/(2*
(-3 + x)))*Log[2] - E^(3/(-3 + x))*x*(1 + Log[2]) + E^(3/(-3 + x))*Log[8]), x])/2 + (27*Defer[Int][E^(3/(-3 +
x))/((3 - x)^2*(E^(x/(-6 + 2*x))*Log[2] - E^(3/(-3 + x))*x*(1 + Log[2]) + E^(3/(-3 + x))*Log[8])), x])/2 - ((2
+ Log[4])*Defer[Int][(E^(3/(-3 + x))*x)/(E^(x/(-6 + 2*x))*Log[2] - E^(3/(-3 + x))*x*(1 + Log[2]) + E^(3/(-3 +
x))*Log[8]), x])/2 + ((18 + Log[512])*Defer[Subst][Defer[Int][1/(E^((3*(x + E^(3/(-3 + x))*(1 + Log[2])))/(3*
E^(3/(-3 + x)) - E^(x/(2*(-3 + x)))*Log[2]))*x), x], x, (E^(x/(2*(-3 + x)))*Log[2] - E^(3/(-3 + x))*x*(1 + Log
[2]) + E^(3/(-3 + x))*Log[8])/(-3 + x)])/(2*(Log[2]/E^(x/(2*(3 - x))) - (3*(1 + Log[2]))/E^(3/(3 - x)) + Log[8
]/E^(3/(3 - x)))) - ((18 + Log[512])*Defer[Subst][Defer[Int][1/(E^((3*(x + E^(3/(-3 + x))*(1 + Log[2])))/(3*E^
(3/(-3 + x)) - E^(x/(2*(-3 + x)))*Log[2]))*x), x], x, (E^(x/(-6 + 2*x))*Log[2] - E^(3/(-3 + x))*x*(1 + Log[2])
+ E^(3/(-3 + x))*Log[8])/(-3 + x)])/(2*(Log[2]/E^(x/(2*(3 - x))) - (3*(1 + Log[2]))/E^(3/(3 - x)) + Log[8]/E^
(3/(3 - x))))

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {3}{-3+x}} \left (-90 x+114 x^2-46 x^3+6 x^4-e^{\frac {-6+x}{-6+2 x}} \left (21 x-21 x^2+4 x^3\right ) \log (2)-\left (198 x-186 x^2+58 x^3-6 x^4\right ) \log (2)-\left (90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} \left (-90+78 x-22 x^2+2 x^3\right ) \log (2)+\left (-270+324 x-144 x^2+28 x^3-2 x^4\right ) \log (2)\right ) \log \left (\frac {-25 x+10 x^2-x^3+e^{\frac {-6+x}{-6+2 x}} \left (25-10 x+x^2\right ) \log (2)+\left (75-55 x+13 x^2-x^3\right ) \log (2)}{\log (2)}\right )\right )}{2 (3-x)^2 (5-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx\\ &=\frac {1}{2} \int \frac {e^{\frac {3}{-3+x}} \left (-90 x+114 x^2-46 x^3+6 x^4-e^{\frac {-6+x}{-6+2 x}} \left (21 x-21 x^2+4 x^3\right ) \log (2)-\left (198 x-186 x^2+58 x^3-6 x^4\right ) \log (2)-\left (90 x-78 x^2+22 x^3-2 x^4+e^{\frac {-6+x}{-6+2 x}} \left (-90+78 x-22 x^2+2 x^3\right ) \log (2)+\left (-270+324 x-144 x^2+28 x^3-2 x^4\right ) \log (2)\right ) \log \left (\frac {-25 x+10 x^2-x^3+e^{\frac {-6+x}{-6+2 x}} \left (25-10 x+x^2\right ) \log (2)+\left (75-55 x+13 x^2-x^3\right ) \log (2)}{\log (2)}\right )\right )}{(3-x)^2 (5-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx\\ &=\frac {1}{2} \int \left (\frac {e^{\frac {3}{-3+x}} x \left (-90+x^3 (2+\log (4))-x^2 (25+\log (33554432))+x (93+\log (5070602400912917605986812821504))-\log (43556142965880123323311949751266331066368)\right )}{(3-x)^2 (5-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}+\frac {21 x-21 x^2+4 x^3-90 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )+78 x \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )-22 x^2 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )+2 x^3 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )}{(-5+x) (-3+x)^2}\right ) \, dx\\ &=\frac {1}{2} \int \frac {e^{\frac {3}{-3+x}} x \left (-90+x^3 (2+\log (4))-x^2 (25+\log (33554432))+x (93+\log (5070602400912917605986812821504))-\log (43556142965880123323311949751266331066368)\right )}{(3-x)^2 (5-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} \int \frac {21 x-21 x^2+4 x^3-90 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )+78 x \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )-22 x^2 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )+2 x^3 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )}{(-5+x) (-3+x)^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{\frac {3}{-3+x}} x \left (-18+x^2 (-2-\log (4))-25 \log (4)+5 \log (33554432)+x (15-5 \log (4)+\log (33554432))-\log (5070602400912917605986812821504)\right )}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} \int \left (\frac {x \left (21-21 x+4 x^2\right )}{(-5+x) (-3+x)^2}+2 \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )\right ) \, dx\\ &=\frac {1}{2} \int \frac {x \left (21-21 x+4 x^2\right )}{(-5+x) (-3+x)^2} \, dx+\frac {1}{2} \int \frac {e^{\frac {3}{-3+x}} x \left (-18-x^2 (2+\log (4))+x (15+\log (32768))-\log (134217728)\right )}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\int \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right ) \, dx\\ &=x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )+\frac {1}{2} \int \left (4+\frac {20}{-5+x}+\frac {9}{(-3+x)^2}+\frac {3}{-3+x}\right ) \, dx+\frac {1}{2} \int \left (\frac {27 e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}+\frac {e^{\frac {3}{-3+x}} x (-2-\log (4))}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}+\frac {6 e^{\frac {3}{-3+x}} \log (4) \left (1-\frac {1+\log (32)}{\log (16)}\right )}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)}+\frac {e^{\frac {3}{-3+x}} (-18-\log (512))}{(3-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}\right ) \, dx-\int \left (\frac {2 x}{-5+x}+\frac {x \left (-1+\frac {3 e^{\frac {-6+x}{2 (-3+x)}}}{2 (-3+x)^2}-\frac {1}{\log (2)}\right )}{e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}}\right ) \, dx\\ &=\frac {9}{2 (3-x)}+2 x+\frac {3}{2} \log (3-x)+10 \log (5-x)+x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )-2 \int \frac {x}{-5+x} \, dx+\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {(3 (1+\log (2)) \log (4)) \int \frac {e^{\frac {3}{-3+x}}}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)} \, dx}{\log (16)}+\frac {1}{2} (-18-\log (512)) \int \frac {e^{\frac {3}{-3+x}}}{(3-x) \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx-\int \frac {x \left (-1+\frac {3 e^{\frac {-6+x}{2 (-3+x)}}}{2 (-3+x)^2}-\frac {1}{\log (2)}\right )}{e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}} \, dx\\ &=\frac {9}{2 (3-x)}+2 x+\frac {3}{2} \log (3-x)+10 \log (5-x)+x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )-2 \int \left (1+\frac {5}{-5+x}\right ) \, dx+\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {(3 (1+\log (2)) \log (4)) \int \frac {e^{\frac {3}{-3+x}}}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)} \, dx}{\log (16)}+\frac {(18+\log (512)) \operatorname {Subst}\left (\int \frac {\exp \left (\frac {3 x}{e^{\frac {x}{-6+2 x}} \log (2)-3 e^{\frac {3}{-3+x}} (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}+\frac {3 e^{\frac {3}{-3+x}} (1+\log (2))}{e^{\frac {x}{-6+2 x}} \log (2)-3 e^{\frac {3}{-3+x}} (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}\right )}{x} \, dx,x,\frac {e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}{-3+x}\right )}{2 \left (-e^{\frac {x}{-6+2 x}} \log (2)+3 e^{\frac {3}{-3+x}} (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)\right )}-\int \left (\frac {3 x}{2 (-3+x)^2}+\frac {e^{\frac {3}{-3+x}} x \left (-18-18 \log (2)+15 x (1+\log (2))-x^2 (2+\log (4))-\log (512)\right )}{2 (3-x)^2 \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}\right ) \, dx\\ &=\frac {9}{2 (3-x)}+\frac {3}{2} \log (3-x)+x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )-\frac {1}{2} \int \frac {e^{\frac {3}{-3+x}} x \left (-18-18 \log (2)+15 x (1+\log (2))-x^2 (2+\log (4))-\log (512)\right )}{(3-x)^2 \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx-\frac {3}{2} \int \frac {x}{(-3+x)^2} \, dx+\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {(3 (1+\log (2)) \log (4)) \int \frac {e^{\frac {3}{-3+x}}}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)} \, dx}{\log (16)}+\frac {(18+\log (512)) \operatorname {Subst}\left (\int \frac {\exp \left (-\frac {3 \left (x+e^{\frac {3}{-3+x}} (1+\log (2))\right )}{3 e^{\frac {3}{-3+x}}-e^{\frac {x}{2 (-3+x)}} \log (2)}\right )}{x} \, dx,x,\frac {e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}{-3+x}\right )}{2 \left (-e^{\frac {x}{-6+2 x}} \log (2)+3 e^{\frac {3}{-3+x}} (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)\right )}\\ &=\frac {9}{2 (3-x)}+\frac {3}{2} \log (3-x)+x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )-\frac {1}{2} \int \left (\frac {27 e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}+\frac {e^{\frac {3}{-3+x}} x (-2-\log (4))}{e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}+\frac {e^{\frac {3}{-3+x}} (3+\log (8))}{e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}+\frac {e^{\frac {3}{-3+x}} (-18-\log (512))}{(3-x) \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )}\right ) \, dx-\frac {3}{2} \int \left (\frac {3}{(-3+x)^2}+\frac {1}{-3+x}\right ) \, dx+\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {(3 (1+\log (2)) \log (4)) \int \frac {e^{\frac {3}{-3+x}}}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)} \, dx}{\log (16)}+\frac {(18+\log (512)) \operatorname {Subst}\left (\int \frac {\exp \left (-\frac {3 \left (x+e^{\frac {3}{-3+x}} (1+\log (2))\right )}{3 e^{\frac {3}{-3+x}}-e^{\frac {x}{2 (-3+x)}} \log (2)}\right )}{x} \, dx,x,\frac {e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}{-3+x}\right )}{2 \left (-e^{\frac {x}{-6+2 x}} \log (2)+3 e^{\frac {3}{-3+x}} (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)\right )}\\ &=x \log \left ((5-x)^2 \left (e^{\frac {6-x}{2 (3-x)}}-\frac {x (1+\log (2))-\log (8)}{\log (2)}\right )\right )-\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {27}{2} \int \frac {e^{\frac {3}{-3+x}}}{(3-x)^2 \left (e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx-\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx+\frac {1}{2} (-2-\log (4)) \int \frac {e^{\frac {3}{-3+x}} x}{e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {1}{2} (3+\log (8)) \int \frac {e^{\frac {3}{-3+x}}}{e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)} \, dx-\frac {(3 (1+\log (2)) \log (4)) \int \frac {e^{\frac {3}{-3+x}}}{-e^{\frac {x}{-6+2 x}} \log (2)+e^{\frac {3}{-3+x}} x (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)} \, dx}{\log (16)}-\frac {1}{2} (-18-\log (512)) \int \frac {e^{\frac {3}{-3+x}}}{(3-x) \left (e^{\frac {x}{2 (-3+x)}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)\right )} \, dx+\frac {(18+\log (512)) \operatorname {Subst}\left (\int \frac {\exp \left (-\frac {3 \left (x+e^{\frac {3}{-3+x}} (1+\log (2))\right )}{3 e^{\frac {3}{-3+x}}-e^{\frac {x}{2 (-3+x)}} \log (2)}\right )}{x} \, dx,x,\frac {e^{\frac {x}{-6+2 x}} \log (2)-e^{\frac {3}{-3+x}} x (1+\log (2))+e^{\frac {3}{-3+x}} \log (8)}{-3+x}\right )}{2 \left (-e^{\frac {x}{-6+2 x}} \log (2)+3 e^{\frac {3}{-3+x}} (1+\log (2))-e^{\frac {3}{-3+x}} \log (8)\right )}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 3.65, size = 46, normalized size = 1.18 \begin {gather*} \frac {1}{2} \left (3+2 x \log \left ((-5+x)^2 \left (e^{\frac {-6+x}{2 (-3+x)}}+\frac {-x (1+\log (2))+\log (8)}{\log (2)}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(90*x - 114*x^2 + 46*x^3 - 6*x^4 + E^((-6 + x)/(-6 + 2*x))*(21*x - 21*x^2 + 4*x^3)*Log[2] + (198*x -
186*x^2 + 58*x^3 - 6*x^4)*Log[2] + (90*x - 78*x^2 + 22*x^3 - 2*x^4 + E^((-6 + x)/(-6 + 2*x))*(-90 + 78*x - 22
*x^2 + 2*x^3)*Log[2] + (-270 + 324*x - 144*x^2 + 28*x^3 - 2*x^4)*Log[2])*Log[(-25*x + 10*x^2 - x^3 + E^((-6 +
x)/(-6 + 2*x))*(25 - 10*x + x^2)*Log[2] + (75 - 55*x + 13*x^2 - x^3)*Log[2])/Log[2]])/(90*x - 78*x^2 + 22*x^3
- 2*x^4 + E^((-6 + x)/(-6 + 2*x))*(-90 + 78*x - 22*x^2 + 2*x^3)*Log[2] + (-270 + 324*x - 144*x^2 + 28*x^3 - 2*
x^4)*Log[2]),x]

[Out]

(3 + 2*x*Log[(-5 + x)^2*(E^((-6 + x)/(2*(-3 + x))) + (-(x*(1 + Log[2])) + Log[8])/Log[2])])/2

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fricas [A]  time = 0.91, size = 60, normalized size = 1.54 \begin {gather*} x \log \left (-\frac {x^{3} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (\frac {x - 6}{2 \, {\left (x - 3\right )}}\right )} \log \relax (2) - 10 \, x^{2} + {\left (x^{3} - 13 \, x^{2} + 55 \, x - 75\right )} \log \relax (2) + 25 \, x}{\log \relax (2)}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22
*x^3-78*x^2+90*x)*log(((x^2-10*x+25)*log(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*log(2)-x^3+10*x^2-25*x)/l
og(2))+(4*x^3-21*x^2+21*x)*log(2)*exp((x-6)/(2*x-6))+(-6*x^4+58*x^3-186*x^2+198*x)*log(2)-6*x^4+46*x^3-114*x^2
+90*x)/((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22*x^3
-78*x^2+90*x),x, algorithm="fricas")

[Out]

x*log(-(x^3 - (x^2 - 10*x + 25)*e^(1/2*(x - 6)/(x - 3))*log(2) - 10*x^2 + (x^3 - 13*x^2 + 55*x - 75)*log(2) +
25*x)/log(2))

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giac [B]  time = 6.01, size = 95, normalized size = 2.44 \begin {gather*} x \log \left (-x^{3} \log \relax (2) + x^{2} e^{\left (-\frac {x}{2 \, {\left (x - 3\right )}} + 1\right )} \log \relax (2) - x^{3} + 13 \, x^{2} \log \relax (2) - 10 \, x e^{\left (-\frac {x}{2 \, {\left (x - 3\right )}} + 1\right )} \log \relax (2) + 10 \, x^{2} - 55 \, x \log \relax (2) + 25 \, e^{\left (-\frac {x}{2 \, {\left (x - 3\right )}} + 1\right )} \log \relax (2) - 25 \, x + 75 \, \log \relax (2)\right ) - x \log \left (\log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22
*x^3-78*x^2+90*x)*log(((x^2-10*x+25)*log(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*log(2)-x^3+10*x^2-25*x)/l
og(2))+(4*x^3-21*x^2+21*x)*log(2)*exp((x-6)/(2*x-6))+(-6*x^4+58*x^3-186*x^2+198*x)*log(2)-6*x^4+46*x^3-114*x^2
+90*x)/((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22*x^3
-78*x^2+90*x),x, algorithm="giac")

[Out]

x*log(-x^3*log(2) + x^2*e^(-1/2*x/(x - 3) + 1)*log(2) - x^3 + 13*x^2*log(2) - 10*x*e^(-1/2*x/(x - 3) + 1)*log(
2) + 10*x^2 - 55*x*log(2) + 25*e^(-1/2*x/(x - 3) + 1)*log(2) - 25*x + 75*log(2)) - x*log(log(2))

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maple [B]  time = 1.55, size = 137, normalized size = 3.51

method	result	size
norman	\(\frac {x^{2} \ln \left (\frac {\left (x^{2}-10 x +25\right ) \ln \relax (2) {\mathrm e}^{\frac {x -6}{2 x -6}}+\left (-x^{3}+13 x^{2}-55 x +75\right ) \ln \relax (2)-x^{3}+10 x^{2}-25 x}{\ln \relax (2)}\right )-3 x \ln \left (\frac {\left (x^{2}-10 x +25\right ) \ln \relax (2) {\mathrm e}^{\frac {x -6}{2 x -6}}+\left (-x^{3}+13 x^{2}-55 x +75\right ) \ln \relax (2)-x^{3}+10 x^{2}-25 x}{\ln \relax (2)}\right )}{x -3}\)	\(137\)
risch	\(x \ln \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )+2 x \ln \left (x -5\right )-i \pi x \mathrm {csgn}\left (i \left (x -5\right )^{2} \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right )^{2}-\frac {i \pi x \mathrm {csgn}\left (i \left (x -5\right )\right )^{2} \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )}{2}+i \pi x \,\mathrm {csgn}\left (i \left (x -5\right )\right ) \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )^{2}-\frac {i \pi x \mathrm {csgn}\left (i \left (x -5\right )^{2}\right )^{3}}{2}-\frac {i \pi x \,\mathrm {csgn}\left (i \left (x -5\right )^{2}\right ) \mathrm {csgn}\left (i \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right ) \mathrm {csgn}\left (i \left (x -5\right )^{2} \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right )}{2}+\frac {i \pi x \,\mathrm {csgn}\left (i \left (x -5\right )^{2}\right ) \mathrm {csgn}\left (i \left (x -5\right )^{2} \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right )^{2}}{2}+\frac {i \pi x \,\mathrm {csgn}\left (i \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right ) \mathrm {csgn}\left (i \left (x -5\right )^{2} \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right )^{2}}{2}+\frac {i \pi x \mathrm {csgn}\left (i \left (x -5\right )^{2} \left (\left (x -{\mathrm e}^{\frac {x -6}{2 x -6}}-3\right ) \ln \relax (2)+x \right )\right )^{3}}{2}+i x \pi -x \ln \left (\ln \relax (2)\right )\)	\(357\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^3-22*x^2+78*x-90)*ln(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*ln(2)-2*x^4+22*x^3-78*
x^2+90*x)*ln(((x^2-10*x+25)*ln(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*ln(2)-x^3+10*x^2-25*x)/ln(2))+(4*x^
3-21*x^2+21*x)*ln(2)*exp((x-6)/(2*x-6))+(-6*x^4+58*x^3-186*x^2+198*x)*ln(2)-6*x^4+46*x^3-114*x^2+90*x)/((2*x^3
-22*x^2+78*x-90)*ln(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*ln(2)-2*x^4+22*x^3-78*x^2+90*x),x,
method=_RETURNVERBOSE)

[Out]

(x^2*ln(((x^2-10*x+25)*ln(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*ln(2)-x^3+10*x^2-25*x)/ln(2))-3*x*ln(((x
^2-10*x+25)*ln(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*ln(2)-x^3+10*x^2-25*x)/ln(2)))/(x-3)

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maxima [B]  time = 0.60, size = 87, normalized size = 2.23 \begin {gather*} -\frac {2 \, x^{2} \log \left (\log \relax (2)\right ) - 2 \, {\left (x^{2} - 3 \, x\right )} \log \left (-{\left (e^{\left (\frac {3}{2 \, {\left (x - 3\right )}}\right )} \log \relax (2) + e^{\left (\frac {3}{2 \, {\left (x - 3\right )}}\right )}\right )} x + e^{\frac {1}{2}} \log \relax (2) + 3 \, e^{\left (\frac {3}{2 \, {\left (x - 3\right )}}\right )} \log \relax (2)\right ) - 4 \, {\left (x^{2} - 3 \, x\right )} \log \left (x - 5\right ) - 6 \, x \log \left (\log \relax (2)\right ) + 9}{2 \, {\left (x - 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22
*x^3-78*x^2+90*x)*log(((x^2-10*x+25)*log(2)*exp((x-6)/(2*x-6))+(-x^3+13*x^2-55*x+75)*log(2)-x^3+10*x^2-25*x)/l
og(2))+(4*x^3-21*x^2+21*x)*log(2)*exp((x-6)/(2*x-6))+(-6*x^4+58*x^3-186*x^2+198*x)*log(2)-6*x^4+46*x^3-114*x^2
+90*x)/((2*x^3-22*x^2+78*x-90)*log(2)*exp((x-6)/(2*x-6))+(-2*x^4+28*x^3-144*x^2+324*x-270)*log(2)-2*x^4+22*x^3
-78*x^2+90*x),x, algorithm="maxima")

[Out]

-1/2*(2*x^2*log(log(2)) - 2*(x^2 - 3*x)*log(-(e^(3/2/(x - 3))*log(2) + e^(3/2/(x - 3)))*x + e^(1/2)*log(2) + 3
*e^(3/2/(x - 3))*log(2)) - 4*(x^2 - 3*x)*log(x - 5) - 6*x*log(log(2)) + 9)/(x - 3)

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mupad [B]  time = 4.76, size = 71, normalized size = 1.82 \begin {gather*} x\,\left (\ln \left (10\,x^2-\ln \relax (2)\,\left (x^3-13\,x^2+55\,x-75\right )-25\,x-x^3+{\mathrm {e}}^{-\frac {6}{2\,x-6}}\,{\mathrm {e}}^{\frac {x}{2\,x-6}}\,\ln \relax (2)\,\left (x^2-10\,x+25\right )\right )-\ln \left (\ln \relax (2)\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((90*x + log(-(25*x + log(2)*(55*x - 13*x^2 + x^3 - 75) - 10*x^2 + x^3 - exp((x - 6)/(2*x - 6))*log(2)*(x^2
- 10*x + 25))/log(2))*(90*x - log(2)*(144*x^2 - 324*x - 28*x^3 + 2*x^4 + 270) - 78*x^2 + 22*x^3 - 2*x^4 + exp
((x - 6)/(2*x - 6))*log(2)*(78*x - 22*x^2 + 2*x^3 - 90)) + log(2)*(198*x - 186*x^2 + 58*x^3 - 6*x^4) - 114*x^2
+ 46*x^3 - 6*x^4 + exp((x - 6)/(2*x - 6))*log(2)*(21*x - 21*x^2 + 4*x^3))/(90*x - log(2)*(144*x^2 - 324*x - 2
8*x^3 + 2*x^4 + 270) - 78*x^2 + 22*x^3 - 2*x^4 + exp((x - 6)/(2*x - 6))*log(2)*(78*x - 22*x^2 + 2*x^3 - 90)),x
)

[Out]

x*(log(10*x^2 - log(2)*(55*x - 13*x^2 + x^3 - 75) - 25*x - x^3 + exp(-6/(2*x - 6))*exp(x/(2*x - 6))*log(2)*(x^
2 - 10*x + 25)) - log(log(2)))

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sympy [B]  time = 1.60, size = 56, normalized size = 1.44 \begin {gather*} x \log {\left (\frac {- x^{3} + 10 x^{2} - 25 x + \left (x^{2} - 10 x + 25\right ) e^{\frac {x - 6}{2 x - 6}} \log {\relax (2 )} + \left (- x^{3} + 13 x^{2} - 55 x + 75\right ) \log {\relax (2 )}}{\log {\relax (2 )}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**3-22*x**2+78*x-90)*ln(2)*exp((x-6)/(2*x-6))+(-2*x**4+28*x**3-144*x**2+324*x-270)*ln(2)-2*x**
4+22*x**3-78*x**2+90*x)*ln(((x**2-10*x+25)*ln(2)*exp((x-6)/(2*x-6))+(-x**3+13*x**2-55*x+75)*ln(2)-x**3+10*x**2
-25*x)/ln(2))+(4*x**3-21*x**2+21*x)*ln(2)*exp((x-6)/(2*x-6))+(-6*x**4+58*x**3-186*x**2+198*x)*ln(2)-6*x**4+46*
x**3-114*x**2+90*x)/((2*x**3-22*x**2+78*x-90)*ln(2)*exp((x-6)/(2*x-6))+(-2*x**4+28*x**3-144*x**2+324*x-270)*ln
(2)-2*x**4+22*x**3-78*x**2+90*x),x)

[Out]

x*log((-x**3 + 10*x**2 - 25*x + (x**2 - 10*x + 25)*exp((x - 6)/(2*x - 6))*log(2) + (-x**3 + 13*x**2 - 55*x + 7
5)*log(2))/log(2))

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