3.84.46 \(\int \frac {-400 x^2+800 x^3-400 x^4+(800 x-1600 x^2+800 x^3) \log (-1+x)+(-400+800 x-400 x^2) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+(-x+x^2) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} (200 x^2-400 x^4+200 x^5+(200 x-400 x^2+800 x^3-400 x^4) \log (-1+x)+(200 x-400 x^2+200 x^3) \log ^2(-1+x))}{e^{\frac {3 (-x+x^2-x^3+(-x+x^2) \log (-1+x))}{x-x^2+(-1+x) \log (-1+x)}} (x^3-2 x^4+x^5+(-2 x^2+4 x^3-2 x^4) \log (-1+x)+(x-2 x^2+x^3) \log ^2(-1+x))+e^{\frac {2 (-x+x^2-x^3+(-x+x^2) \log (-1+x))}{x-x^2+(-1+x) \log (-1+x)}} (-3 x^3+6 x^4-3 x^5+(6 x^2-12 x^3+6 x^4) \log (-1+x)+(-3 x+6 x^2-3 x^3) \log ^2(-1+x)) \log (x^2)+e^{\frac {-x+x^2-x^3+(-x+x^2) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} (3 x^3-6 x^4+3 x^5+(-6 x^2+12 x^3-6 x^4) \log (-1+x)+(3 x-6 x^2+3 x^3) \log ^2(-1+x)) \log ^2(x^2)+(-x^3+2 x^4-x^5+(2 x^2-4 x^3+2 x^4) \log (-1+x)+(-x+2 x^2-x^3) \log ^2(-1+x)) \log ^3(x^2)} \, dx\)
Optimal. Leaf size=34 \[ 1-\frac {100}{\left (-e^{x+\frac {x}{(-1+x) (x-\log (-1+x))}}+\log \left (x^2\right )\right )^2} \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-400*x^2 + 800*x^3 - 400*x^4 + (800*x - 1600*x^2 + 800*x^3)*Log[-1 + x] + (-400 + 800*x - 400*x^2)*Log[-1
+ x]^2 + E^((-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(200*x^2 - 400*x^4 +
200*x^5 + (200*x - 400*x^2 + 800*x^3 - 400*x^4)*Log[-1 + x] + (200*x - 400*x^2 + 200*x^3)*Log[-1 + x]^2))/(E^(
(3*(-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(x^3 - 2*x^4 + x^5 + (-2*x^2 +
4*x^3 - 2*x^4)*Log[-1 + x] + (x - 2*x^2 + x^3)*Log[-1 + x]^2) + E^((2*(-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x
]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(-3*x^3 + 6*x^4 - 3*x^5 + (6*x^2 - 12*x^3 + 6*x^4)*Log[-1 + x] + (-3*x +
6*x^2 - 3*x^3)*Log[-1 + x]^2)*Log[x^2] + E^((-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x])/(x - x^2 + (-1 + x)*Log
[-1 + x]))*(3*x^3 - 6*x^4 + 3*x^5 + (-6*x^2 + 12*x^3 - 6*x^4)*Log[-1 + x] + (3*x - 6*x^2 + 3*x^3)*Log[-1 + x]^
2)*Log[x^2]^2 + (-x^3 + 2*x^4 - x^5 + (2*x^2 - 4*x^3 + 2*x^4)*Log[-1 + x] + (-x + 2*x^2 - x^3)*Log[-1 + x]^2)*
Log[x^2]^3),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 1.16, size = 47, normalized size = 1.38 \begin {gather*} -\frac {100}{\left (e^{\frac {x \left (1-x+x^2-(-1+x) \log (-1+x)\right )}{(-1+x) (x-\log (-1+x))}}-\log \left (x^2\right )\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-400*x^2 + 800*x^3 - 400*x^4 + (800*x - 1600*x^2 + 800*x^3)*Log[-1 + x] + (-400 + 800*x - 400*x^2)*
Log[-1 + x]^2 + E^((-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(200*x^2 - 400*
x^4 + 200*x^5 + (200*x - 400*x^2 + 800*x^3 - 400*x^4)*Log[-1 + x] + (200*x - 400*x^2 + 200*x^3)*Log[-1 + x]^2)
)/(E^((3*(-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(x^3 - 2*x^4 + x^5 + (-2
*x^2 + 4*x^3 - 2*x^4)*Log[-1 + x] + (x - 2*x^2 + x^3)*Log[-1 + x]^2) + E^((2*(-x + x^2 - x^3 + (-x + x^2)*Log[
-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(-3*x^3 + 6*x^4 - 3*x^5 + (6*x^2 - 12*x^3 + 6*x^4)*Log[-1 + x] + (
-3*x + 6*x^2 - 3*x^3)*Log[-1 + x]^2)*Log[x^2] + E^((-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x])/(x - x^2 + (-1 +
x)*Log[-1 + x]))*(3*x^3 - 6*x^4 + 3*x^5 + (-6*x^2 + 12*x^3 - 6*x^4)*Log[-1 + x] + (3*x - 6*x^2 + 3*x^3)*Log[-1
+ x]^2)*Log[x^2]^2 + (-x^3 + 2*x^4 - x^5 + (2*x^2 - 4*x^3 + 2*x^4)*Log[-1 + x] + (-x + 2*x^2 - x^3)*Log[-1 +
x]^2)*Log[x^2]^3),x]
[Out]
-100/(E^((x*(1 - x + x^2 - (-1 + x)*Log[-1 + x]))/((-1 + x)*(x - Log[-1 + x]))) - Log[x^2])^2
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fricas [B] time = 0.82, size = 108, normalized size = 3.18 \begin {gather*} \frac {100}{2 \, e^{\left (\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (x - 1\right ) + x}{x^{2} - {\left (x - 1\right )} \log \left (x - 1\right ) - x}\right )} \log \left (x^{2}\right ) - \log \left (x^{2}\right )^{2} - e^{\left (\frac {2 \, {\left (x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (x - 1\right ) + x\right )}}{x^{2} - {\left (x - 1\right )} \log \left (x - 1\right ) - x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((200*x^3-400*x^2+200*x)*log(x-1)^2+(-400*x^4+800*x^3-400*x^2+200*x)*log(x-1)+200*x^5-400*x^4+200*x
^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))+(-400*x^2+800*x-400)*log(x-1)^2+(800*x^3-1600*x^2
+800*x)*log(x-1)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(x-1)^2+(-2*x^4+4*x^3-2*x^2)*log(x-1)+x^5-2*x^4+x
^3)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(x-1)^2+(6*x^4-12*x^3+6*
x^2)*log(x-1)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^2+((3*x^3-6
*x^2+3*x)*log(x-1)^2+(-6*x^4+12*x^3-6*x^2)*log(x-1)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*log(x-1)-x^3+x^
2-x)/((x-1)*log(x-1)-x^2+x))+((-x^3+2*x^2-x)*log(x-1)^2+(2*x^4-4*x^3+2*x^2)*log(x-1)-x^5+2*x^4-x^3)*log(x^2)^3
),x, algorithm="fricas")
[Out]
100/(2*e^((x^3 - x^2 - (x^2 - x)*log(x - 1) + x)/(x^2 - (x - 1)*log(x - 1) - x))*log(x^2) - log(x^2)^2 - e^(2*
(x^3 - x^2 - (x^2 - x)*log(x - 1) + x)/(x^2 - (x - 1)*log(x - 1) - x)))
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((200*x^3-400*x^2+200*x)*log(x-1)^2+(-400*x^4+800*x^3-400*x^2+200*x)*log(x-1)+200*x^5-400*x^4+200*x
^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))+(-400*x^2+800*x-400)*log(x-1)^2+(800*x^3-1600*x^2
+800*x)*log(x-1)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(x-1)^2+(-2*x^4+4*x^3-2*x^2)*log(x-1)+x^5-2*x^4+x
^3)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(x-1)^2+(6*x^4-12*x^3+6*
x^2)*log(x-1)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^2+((3*x^3-6
*x^2+3*x)*log(x-1)^2+(-6*x^4+12*x^3-6*x^2)*log(x-1)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*log(x-1)-x^3+x^
2-x)/((x-1)*log(x-1)-x^2+x))+((-x^3+2*x^2-x)*log(x-1)^2+(2*x^4-4*x^3+2*x^2)*log(x-1)-x^5+2*x^4-x^3)*log(x^2)^3
),x, algorithm="giac")
[Out]
Timed out
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maple [F] time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (200 x^{3}-400 x^{2}+200 x \right ) \ln \left (x -1\right )^{2}+\left (-400 x^{4}+800 x^{3}-400 x^{2}+200 x \right ) \ln \left (x -1\right )+200 x^{5}-400 x^{4}+200 x^{2}\right ) {\mathrm e}^{\frac {\left (x^{2}-x \right ) \ln \left (x -1\right )-x^{3}+x^{2}-x}{\left (x -1\right ) \ln \left (x -1\right )-x^{2}+x}}+\left (-400 x^{2}+800 x -400\right ) \ln \left (x -1\right )^{2}+\left (800 x^{3}-1600 x^{2}+800 x \right ) \ln \left (x -1\right )-400 x^{4}+800 x^{3}-400 x^{2}}{\left (\left (x^{3}-2 x^{2}+x \right ) \ln \left (x -1\right )^{2}+\left (-2 x^{4}+4 x^{3}-2 x^{2}\right ) \ln \left (x -1\right )+x^{5}-2 x^{4}+x^{3}\right ) {\mathrm e}^{\frac {3 \left (x^{2}-x \right ) \ln \left (x -1\right )-3 x^{3}+3 x^{2}-3 x}{\left (x -1\right ) \ln \left (x -1\right )-x^{2}+x}}+\left (\left (-3 x^{3}+6 x^{2}-3 x \right ) \ln \left (x -1\right )^{2}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) \ln \left (x -1\right )-3 x^{5}+6 x^{4}-3 x^{3}\right ) \ln \left (x^{2}\right ) {\mathrm e}^{\frac {2 \left (x^{2}-x \right ) \ln \left (x -1\right )-2 x^{3}+2 x^{2}-2 x}{\left (x -1\right ) \ln \left (x -1\right )-x^{2}+x}}+\left (\left (3 x^{3}-6 x^{2}+3 x \right ) \ln \left (x -1\right )^{2}+\left (-6 x^{4}+12 x^{3}-6 x^{2}\right ) \ln \left (x -1\right )+3 x^{5}-6 x^{4}+3 x^{3}\right ) \ln \left (x^{2}\right )^{2} {\mathrm e}^{\frac {\left (x^{2}-x \right ) \ln \left (x -1\right )-x^{3}+x^{2}-x}{\left (x -1\right ) \ln \left (x -1\right )-x^{2}+x}}+\left (\left (-x^{3}+2 x^{2}-x \right ) \ln \left (x -1\right )^{2}+\left (2 x^{4}-4 x^{3}+2 x^{2}\right ) \ln \left (x -1\right )-x^{5}+2 x^{4}-x^{3}\right ) \ln \left (x^{2}\right )^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((200*x^3-400*x^2+200*x)*ln(x-1)^2+(-400*x^4+800*x^3-400*x^2+200*x)*ln(x-1)+200*x^5-400*x^4+200*x^2)*exp(
((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))+(-400*x^2+800*x-400)*ln(x-1)^2+(800*x^3-1600*x^2+800*x)*ln(
x-1)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*ln(x-1)^2+(-2*x^4+4*x^3-2*x^2)*ln(x-1)+x^5-2*x^4+x^3)*exp(((x^2-
x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*ln(x-1)^2+(6*x^4-12*x^3+6*x^2)*ln(x-1)-3*x^
5+6*x^4-3*x^3)*ln(x^2)*exp(((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))^2+((3*x^3-6*x^2+3*x)*ln(x-1)^2+(
-6*x^4+12*x^3-6*x^2)*ln(x-1)+3*x^5-6*x^4+3*x^3)*ln(x^2)^2*exp(((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x
))+((-x^3+2*x^2-x)*ln(x-1)^2+(2*x^4-4*x^3+2*x^2)*ln(x-1)-x^5+2*x^4-x^3)*ln(x^2)^3),x)
[Out]
int((((200*x^3-400*x^2+200*x)*ln(x-1)^2+(-400*x^4+800*x^3-400*x^2+200*x)*ln(x-1)+200*x^5-400*x^4+200*x^2)*exp(
((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))+(-400*x^2+800*x-400)*ln(x-1)^2+(800*x^3-1600*x^2+800*x)*ln(
x-1)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*ln(x-1)^2+(-2*x^4+4*x^3-2*x^2)*ln(x-1)+x^5-2*x^4+x^3)*exp(((x^2-
x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*ln(x-1)^2+(6*x^4-12*x^3+6*x^2)*ln(x-1)-3*x^
5+6*x^4-3*x^3)*ln(x^2)*exp(((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x))^2+((3*x^3-6*x^2+3*x)*ln(x-1)^2+(
-6*x^4+12*x^3-6*x^2)*ln(x-1)+3*x^5-6*x^4+3*x^3)*ln(x^2)^2*exp(((x^2-x)*ln(x-1)-x^3+x^2-x)/((x-1)*ln(x-1)-x^2+x
))+((-x^3+2*x^2-x)*ln(x-1)^2+(2*x^4-4*x^3+2*x^2)*ln(x-1)-x^5+2*x^4-x^3)*ln(x^2)^3),x)
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maxima [B] time = 3.20, size = 140, normalized size = 4.12 \begin {gather*} -\frac {100 \, e^{\left (\frac {2}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )}}{4 \, e^{\left (\frac {2}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )} \log \relax (x)^{2} - 4 \, e^{\left (x + \frac {\log \left (x - 1\right )}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right )^{2} + \log \left (x - 1\right )} + \frac {1}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )} \log \relax (x) + e^{\left (2 \, x + \frac {2 \, \log \left (x - 1\right )}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right )^{2} + \log \left (x - 1\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((200*x^3-400*x^2+200*x)*log(x-1)^2+(-400*x^4+800*x^3-400*x^2+200*x)*log(x-1)+200*x^5-400*x^4+200*x
^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))+(-400*x^2+800*x-400)*log(x-1)^2+(800*x^3-1600*x^2
+800*x)*log(x-1)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(x-1)^2+(-2*x^4+4*x^3-2*x^2)*log(x-1)+x^5-2*x^4+x
^3)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(x-1)^2+(6*x^4-12*x^3+6*
x^2)*log(x-1)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(x-1)-x^3+x^2-x)/((x-1)*log(x-1)-x^2+x))^2+((3*x^3-6
*x^2+3*x)*log(x-1)^2+(-6*x^4+12*x^3-6*x^2)*log(x-1)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*log(x-1)-x^3+x^
2-x)/((x-1)*log(x-1)-x^2+x))+((-x^3+2*x^2-x)*log(x-1)^2+(2*x^4-4*x^3+2*x^2)*log(x-1)-x^5+2*x^4-x^3)*log(x^2)^3
),x, algorithm="maxima")
[Out]
-100*e^(2/(x*(log(x - 1) - 1) - log(x - 1) + 1))/(4*e^(2/(x*(log(x - 1) - 1) - log(x - 1) + 1))*log(x)^2 - 4*e
^(x + log(x - 1)/(x*(log(x - 1) - 1) - log(x - 1)^2 + log(x - 1)) + 1/(x*(log(x - 1) - 1) - log(x - 1) + 1))*l
og(x) + e^(2*x + 2*log(x - 1)/(x*(log(x - 1) - 1) - log(x - 1)^2 + log(x - 1))))
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mupad [B] time = 6.05, size = 212, normalized size = 6.24 \begin {gather*} -\frac {100}{{\ln \left (x^2\right )}^2+\frac {{\mathrm {e}}^{-\frac {2\,x}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{\frac {2\,x^2}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{-\frac {2\,x^3}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}}{{\left (x-1\right )}^{\frac {2\,x}{x-\ln \left (x-1\right )}}}-\frac {2\,\ln \left (x^2\right )\,{\mathrm {e}}^{-\frac {x}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{\frac {x^2}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{-\frac {x^3}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}}{{\left (x-1\right )}^{\frac {x}{x-\ln \left (x-1\right )}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(x - 1)*(800*x - 1600*x^2 + 800*x^3) - log(x - 1)^2*(400*x^2 - 800*x + 400) + exp(-(x + log(x - 1)*(x
- x^2) - x^2 + x^3)/(x + log(x - 1)*(x - 1) - x^2))*(log(x - 1)*(200*x - 400*x^2 + 800*x^3 - 400*x^4) + log(x
- 1)^2*(200*x - 400*x^2 + 200*x^3) + 200*x^2 - 400*x^4 + 200*x^5) - 400*x^2 + 800*x^3 - 400*x^4)/(exp(-(3*(x +
log(x - 1)*(x - x^2) - x^2 + x^3))/(x + log(x - 1)*(x - 1) - x^2))*(x^3 - log(x - 1)*(2*x^2 - 4*x^3 + 2*x^4)
- 2*x^4 + x^5 + log(x - 1)^2*(x - 2*x^2 + x^3)) - log(x^2)^3*(x^3 - log(x - 1)*(2*x^2 - 4*x^3 + 2*x^4) - 2*x^4
+ x^5 + log(x - 1)^2*(x - 2*x^2 + x^3)) - log(x^2)*exp(-(2*(x + log(x - 1)*(x - x^2) - x^2 + x^3))/(x + log(x
- 1)*(x - 1) - x^2))*(log(x - 1)^2*(3*x - 6*x^2 + 3*x^3) - log(x - 1)*(6*x^2 - 12*x^3 + 6*x^4) + 3*x^3 - 6*x^
4 + 3*x^5) + log(x^2)^2*exp(-(x + log(x - 1)*(x - x^2) - x^2 + x^3)/(x + log(x - 1)*(x - 1) - x^2))*(log(x - 1
)^2*(3*x - 6*x^2 + 3*x^3) - log(x - 1)*(6*x^2 - 12*x^3 + 6*x^4) + 3*x^3 - 6*x^4 + 3*x^5)),x)
[Out]
-100/(log(x^2)^2 + (exp(-(2*x)/(x - log(x - 1) + x*log(x - 1) - x^2))*exp((2*x^2)/(x - log(x - 1) + x*log(x -
1) - x^2))*exp(-(2*x^3)/(x - log(x - 1) + x*log(x - 1) - x^2)))/(x - 1)^((2*x)/(x - log(x - 1))) - (2*log(x^2)
*exp(-x/(x - log(x - 1) + x*log(x - 1) - x^2))*exp(x^2/(x - log(x - 1) + x*log(x - 1) - x^2))*exp(-x^3/(x - lo
g(x - 1) + x*log(x - 1) - x^2)))/(x - 1)^(x/(x - log(x - 1))))
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sympy [B] time = 4.75, size = 90, normalized size = 2.65 \begin {gather*} - \frac {100}{e^{\frac {2 \left (- x^{3} + x^{2} - x + \left (x^{2} - x\right ) \log {\left (x - 1 \right )}\right )}{- x^{2} + x + \left (x - 1\right ) \log {\left (x - 1 \right )}}} - 2 e^{\frac {- x^{3} + x^{2} - x + \left (x^{2} - x\right ) \log {\left (x - 1 \right )}}{- x^{2} + x + \left (x - 1\right ) \log {\left (x - 1 \right )}}} \log {\left (x^{2} \right )} + \log {\left (x^{2} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((200*x**3-400*x**2+200*x)*ln(x-1)**2+(-400*x**4+800*x**3-400*x**2+200*x)*ln(x-1)+200*x**5-400*x**4
+200*x**2)*exp(((x**2-x)*ln(x-1)-x**3+x**2-x)/((x-1)*ln(x-1)-x**2+x))+(-400*x**2+800*x-400)*ln(x-1)**2+(800*x*
*3-1600*x**2+800*x)*ln(x-1)-400*x**4+800*x**3-400*x**2)/(((x**3-2*x**2+x)*ln(x-1)**2+(-2*x**4+4*x**3-2*x**2)*l
n(x-1)+x**5-2*x**4+x**3)*exp(((x**2-x)*ln(x-1)-x**3+x**2-x)/((x-1)*ln(x-1)-x**2+x))**3+((-3*x**3+6*x**2-3*x)*l
n(x-1)**2+(6*x**4-12*x**3+6*x**2)*ln(x-1)-3*x**5+6*x**4-3*x**3)*ln(x**2)*exp(((x**2-x)*ln(x-1)-x**3+x**2-x)/((
x-1)*ln(x-1)-x**2+x))**2+((3*x**3-6*x**2+3*x)*ln(x-1)**2+(-6*x**4+12*x**3-6*x**2)*ln(x-1)+3*x**5-6*x**4+3*x**3
)*ln(x**2)**2*exp(((x**2-x)*ln(x-1)-x**3+x**2-x)/((x-1)*ln(x-1)-x**2+x))+((-x**3+2*x**2-x)*ln(x-1)**2+(2*x**4-
4*x**3+2*x**2)*ln(x-1)-x**5+2*x**4-x**3)*ln(x**2)**3),x)
[Out]
-100/(exp(2*(-x**3 + x**2 - x + (x**2 - x)*log(x - 1))/(-x**2 + x + (x - 1)*log(x - 1))) - 2*exp((-x**3 + x**2
- x + (x**2 - x)*log(x - 1))/(-x**2 + x + (x - 1)*log(x - 1)))*log(x**2) + log(x**2)**2)
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