3.90.26 \(\int \frac {-1250+1300 x-440 x^2+48 x^3+e^{3-x} (100-112 x+38 x^2-4 x^3)+(-250+250 x-80 x^2+8 x^3+e^{3-x} (20-18 x+4 x^2)) \log (\frac {-25+e^{3-x} (2-x)+15 x-2 x^2}{-5+2 x})}{-625 x+625 x^2-200 x^3+20 x^4+e^{3-x} (50 x-45 x^2+10 x^3)+(-125 x+125 x^2-40 x^3+4 x^4+e^{3-x} (10 x-9 x^2+2 x^3)) \log (\frac {-25+e^{3-x} (2-x)+15 x-2 x^2}{-5+2 x})} \, dx\)

Optimal. Leaf size=33 \[ 2 \log \left (x \left (5+\log \left (5-x+\frac {e^{3-x} (2-x)}{-5+2 x}\right )\right )\right ) \]

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Rubi [F]  time = 25.02, 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 {-1250+1300 x-440 x^2+48 x^3+e^{3-x} \left (100-112 x+38 x^2-4 x^3\right )+\left (-250+250 x-80 x^2+8 x^3+e^{3-x} \left (20-18 x+4 x^2\right )\right ) \log \left (\frac {-25+e^{3-x} (2-x)+15 x-2 x^2}{-5+2 x}\right )}{-625 x+625 x^2-200 x^3+20 x^4+e^{3-x} \left (50 x-45 x^2+10 x^3\right )+\left (-125 x+125 x^2-40 x^3+4 x^4+e^{3-x} \left (10 x-9 x^2+2 x^3\right )\right ) \log \left (\frac {-25+e^{3-x} (2-x)+15 x-2 x^2}{-5+2 x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1250 + 1300*x - 440*x^2 + 48*x^3 + E^(3 - x)*(100 - 112*x + 38*x^2 - 4*x^3) + (-250 + 250*x - 80*x^2 + 8
*x^3 + E^(3 - x)*(20 - 18*x + 4*x^2))*Log[(-25 + E^(3 - x)*(2 - x) + 15*x - 2*x^2)/(-5 + 2*x)])/(-625*x + 625*
x^2 - 200*x^3 + 20*x^4 + E^(3 - x)*(50*x - 45*x^2 + 10*x^3) + (-125*x + 125*x^2 - 40*x^3 + 4*x^4 + E^(3 - x)*(
10*x - 9*x^2 + 2*x^3))*Log[(-25 + E^(3 - x)*(2 - x) + 15*x - 2*x^2)/(-5 + 2*x)]),x]

[Out]

2*Log[x] - 2*Defer[Int][(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])^(-1), x] + 2*Defer[I
nt][1/((-2 + x)*(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])), x] - 4*Defer[Int][1/((-5 +
2*x)*(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])), x] + 42*Defer[Int][E^x/((-2*E^3 + 25
*E^x + E^3*x - 15*E^x*x + 2*E^x*x^2)*(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])), x] -
6*Defer[Int][E^x/((-2 + x)*(-2*E^3 + 25*E^x + E^3*x - 15*E^x*x + 2*E^x*x^2)*(5 + Log[-((25 + E^(3 - x)*(-2 + x
) - 15*x + 2*x^2)/(-5 + 2*x))])), x] - 26*Defer[Int][(E^x*x)/((-2*E^3 + 25*E^x + E^3*x - 15*E^x*x + 2*E^x*x^2)
*(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])), x] + 4*Defer[Int][(E^x*x^2)/((-2*E^3 + 25
*E^x + E^3*x - 15*E^x*x + 2*E^x*x^2)*(5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (-1250+1300 x-440 x^2+48 x^3+e^{3-x} \left (100-112 x+38 x^2-4 x^3\right )+\left (-250+250 x-80 x^2+8 x^3+e^{3-x} \left (20-18 x+4 x^2\right )\right ) \log \left (\frac {-25+e^{3-x} (2-x)+15 x-2 x^2}{-5+2 x}\right )\right )}{(5-2 x) x \left (2 e^3-25 e^x-e^3 x+15 e^x x-2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ &=\int \left (\frac {2 e^x \left (-45+47 x-17 x^2+2 x^3\right )}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}-\frac {2 \left (-50+56 x-19 x^2+2 x^3-10 \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )+9 x \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )-2 x^2 \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}{(-2+x) x (-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}\right ) \, dx\\ &=2 \int \frac {e^x \left (-45+47 x-17 x^2+2 x^3\right )}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-2 \int \frac {-50+56 x-19 x^2+2 x^3-10 \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )+9 x \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )-2 x^2 \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )}{(-2+x) x (-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ &=-\left (2 \int \frac {-50+56 x-19 x^2+2 x^3+\left (-10+9 x-2 x^2\right ) \log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )}{(5-2 x) (2-x) x \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\right )+2 \int \left (\frac {21 e^x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}-\frac {3 e^x}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}-\frac {13 e^x x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}+\frac {2 e^x x^2}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}\right ) \, dx\\ &=-\left (2 \int \left (-\frac {1}{x}+\frac {11-9 x+2 x^2}{(-2+x) (-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}\right ) \, dx\right )+4 \int \frac {e^x x^2}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-6 \int \frac {e^x}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-26 \int \frac {e^x x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+42 \int \frac {e^x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ &=2 \log (x)-2 \int \frac {11-9 x+2 x^2}{(-2+x) (-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+4 \int \frac {e^x x^2}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-6 \int \frac {e^x}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-26 \int \frac {e^x x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+42 \int \frac {e^x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ &=2 \log (x)-2 \int \left (\frac {1}{5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )}-\frac {1}{(-2+x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}+\frac {2}{(-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )}\right ) \, dx+4 \int \frac {e^x x^2}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-6 \int \frac {e^x}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-26 \int \frac {e^x x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+42 \int \frac {e^x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ &=2 \log (x)-2 \int \frac {1}{5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )} \, dx+2 \int \frac {1}{(-2+x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-4 \int \frac {1}{(-5+2 x) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+4 \int \frac {e^x x^2}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-6 \int \frac {e^x}{(-2+x) \left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx-26 \int \frac {e^x x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx+42 \int \frac {e^x}{\left (-2 e^3+25 e^x+e^3 x-15 e^x x+2 e^x x^2\right ) \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.20, size = 39, normalized size = 1.18 \begin {gather*} 2 \left (\log (x)+\log \left (5+\log \left (-\frac {25+e^{3-x} (-2+x)-15 x+2 x^2}{-5+2 x}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1250 + 1300*x - 440*x^2 + 48*x^3 + E^(3 - x)*(100 - 112*x + 38*x^2 - 4*x^3) + (-250 + 250*x - 80*x
^2 + 8*x^3 + E^(3 - x)*(20 - 18*x + 4*x^2))*Log[(-25 + E^(3 - x)*(2 - x) + 15*x - 2*x^2)/(-5 + 2*x)])/(-625*x
+ 625*x^2 - 200*x^3 + 20*x^4 + E^(3 - x)*(50*x - 45*x^2 + 10*x^3) + (-125*x + 125*x^2 - 40*x^3 + 4*x^4 + E^(3
- x)*(10*x - 9*x^2 + 2*x^3))*Log[(-25 + E^(3 - x)*(2 - x) + 15*x - 2*x^2)/(-5 + 2*x)]),x]

[Out]

2*(Log[x] + Log[5 + Log[-((25 + E^(3 - x)*(-2 + x) - 15*x + 2*x^2)/(-5 + 2*x))]])

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fricas [A]  time = 0.52, size = 40, normalized size = 1.21 \begin {gather*} 2 \, \log \relax (x) + 2 \, \log \left (\log \left (-\frac {2 \, x^{2} + {\left (x - 2\right )} e^{\left (-x + 3\right )} - 15 \, x + 25}{2 \, x - 5}\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2-18*x+20)*exp(3-x)+8*x^3-80*x^2+250*x-250)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(-4*x
^3+38*x^2-112*x+100)*exp(3-x)+48*x^3-440*x^2+1300*x-1250)/(((2*x^3-9*x^2+10*x)*exp(3-x)+4*x^4-40*x^3+125*x^2-1
25*x)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(10*x^3-45*x^2+50*x)*exp(3-x)+20*x^4-200*x^3+625*x^2-625*x),
x, algorithm="fricas")

[Out]

2*log(x) + 2*log(log(-(2*x^2 + (x - 2)*e^(-x + 3) - 15*x + 25)/(2*x - 5)) + 5)

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giac [A]  time = 0.71, size = 46, normalized size = 1.39 \begin {gather*} 2 \, \log \relax (x) + 2 \, \log \left (\log \left (-\frac {2 \, x^{2} + x e^{\left (-x + 3\right )} - 15 \, x - 2 \, e^{\left (-x + 3\right )} + 25}{2 \, x - 5}\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2-18*x+20)*exp(3-x)+8*x^3-80*x^2+250*x-250)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(-4*x
^3+38*x^2-112*x+100)*exp(3-x)+48*x^3-440*x^2+1300*x-1250)/(((2*x^3-9*x^2+10*x)*exp(3-x)+4*x^4-40*x^3+125*x^2-1
25*x)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(10*x^3-45*x^2+50*x)*exp(3-x)+20*x^4-200*x^3+625*x^2-625*x),
x, algorithm="giac")

[Out]

2*log(x) + 2*log(log(-(2*x^2 + x*e^(-x + 3) - 15*x - 2*e^(-x + 3) + 25)/(2*x - 5)) + 5)

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maple [A]  time = 0.27, size = 42, normalized size = 1.27

method	result	size
norman	\(2 \ln \relax (x )+2 \ln \left (\ln \left (\frac {\left (2-x \right ) {\mathrm e}^{3-x}-2 x^{2}+15 x -25}{2 x -5}\right )+5\right )\)	\(42\)
risch	\(2 \ln \relax (x )+2 \ln \left (\ln \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )+\frac {i \left (-2 \pi \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )}{x -\frac {5}{2}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{x -\frac {5}{2}}\right ) \mathrm {csgn}\left (i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )}{x -\frac {5}{2}}\right )+\pi \,\mathrm {csgn}\left (\frac {i}{x -\frac {5}{2}}\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )}{x -\frac {5}{2}}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )}{x -\frac {5}{2}}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\frac {{\mathrm e}^{3-x}}{2}-\frac {15}{2}\right ) x -{\mathrm e}^{3-x}+\frac {25}{2}\right )}{x -\frac {5}{2}}\right )^{3}+2 \pi +2 i \ln \left (x -\frac {5}{2}\right )-10 i\right )}{2}\right )\)	\(318\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^2-18*x+20)*exp(3-x)+8*x^3-80*x^2+250*x-250)*ln(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(-4*x^3+38*x
^2-112*x+100)*exp(3-x)+48*x^3-440*x^2+1300*x-1250)/(((2*x^3-9*x^2+10*x)*exp(3-x)+4*x^4-40*x^3+125*x^2-125*x)*l
n(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(10*x^3-45*x^2+50*x)*exp(3-x)+20*x^4-200*x^3+625*x^2-625*x),x,method
=_RETURNVERBOSE)

[Out]

2*ln(x)+2*ln(ln(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+5)

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maxima [A]  time = 0.63, size = 46, normalized size = 1.39 \begin {gather*} 2 \, \log \relax (x) + 2 \, \log \left (-x + \log \left (-x e^{3} - {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{x} + 2 \, e^{3}\right ) - \log \left (2 \, x - 5\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2-18*x+20)*exp(3-x)+8*x^3-80*x^2+250*x-250)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(-4*x
^3+38*x^2-112*x+100)*exp(3-x)+48*x^3-440*x^2+1300*x-1250)/(((2*x^3-9*x^2+10*x)*exp(3-x)+4*x^4-40*x^3+125*x^2-1
25*x)*log(((2-x)*exp(3-x)-2*x^2+15*x-25)/(2*x-5))+(10*x^3-45*x^2+50*x)*exp(3-x)+20*x^4-200*x^3+625*x^2-625*x),
x, algorithm="maxima")

[Out]

2*log(x) + 2*log(-x + log(-x*e^3 - (2*x^2 - 15*x + 25)*e^x + 2*e^3) - log(2*x - 5) + 5)

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mupad [B]  time = 7.19, size = 40, normalized size = 1.21 \begin {gather*} 2\,\ln \left (\ln \left (-\frac {2\,x^2-15\,x+{\mathrm {e}}^{-x}\,{\mathrm {e}}^3\,\left (x-2\right )+25}{2\,x-5}\right )+5\right )+2\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1300*x + log(-(exp(3 - x)*(x - 2) - 15*x + 2*x^2 + 25)/(2*x - 5))*(250*x + exp(3 - x)*(4*x^2 - 18*x + 20)
- 80*x^2 + 8*x^3 - 250) - exp(3 - x)*(112*x - 38*x^2 + 4*x^3 - 100) - 440*x^2 + 48*x^3 - 1250)/(log(-(exp(3 -
x)*(x - 2) - 15*x + 2*x^2 + 25)/(2*x - 5))*(exp(3 - x)*(10*x - 9*x^2 + 2*x^3) - 125*x + 125*x^2 - 40*x^3 + 4*
x^4) - 625*x + exp(3 - x)*(50*x - 45*x^2 + 10*x^3) + 625*x^2 - 200*x^3 + 20*x^4),x)

[Out]

2*log(log(-(2*x^2 - 15*x + exp(-x)*exp(3)*(x - 2) + 25)/(2*x - 5)) + 5) + 2*log(x)

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sympy [A]  time = 1.03, size = 34, normalized size = 1.03 \begin {gather*} 2 \log {\relax (x )} + 2 \log {\left (\log {\left (\frac {- 2 x^{2} + 15 x + \left (2 - x\right ) e^{3 - x} - 25}{2 x - 5} \right )} + 5 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**2-18*x+20)*exp(3-x)+8*x**3-80*x**2+250*x-250)*ln(((2-x)*exp(3-x)-2*x**2+15*x-25)/(2*x-5))+(-
4*x**3+38*x**2-112*x+100)*exp(3-x)+48*x**3-440*x**2+1300*x-1250)/(((2*x**3-9*x**2+10*x)*exp(3-x)+4*x**4-40*x**
3+125*x**2-125*x)*ln(((2-x)*exp(3-x)-2*x**2+15*x-25)/(2*x-5))+(10*x**3-45*x**2+50*x)*exp(3-x)+20*x**4-200*x**3
+625*x**2-625*x),x)

[Out]

2*log(x) + 2*log(log((-2*x**2 + 15*x + (2 - x)*exp(3 - x) - 25)/(2*x - 5)) + 5)

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