3.68.41 \(\int \frac {e^{x^4 \log ^2(\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2})} ((-10 x^5+20 x^6-10 x^7+\sqrt [5]{\frac {1}{x}} (12 x^3-22 x^4)) \log (\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2})+(-20 x^5+40 x^6-20 x^7+\sqrt [5]{\frac {1}{x}} (-20 x^3+20 x^4)) \log ^2(\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2}))}{-5 x^2+10 x^3-5 x^4+\sqrt [5]{\frac {1}{x}} (-5+5 x)} \, dx\)

Optimal. Leaf size=30 \[ e^{x^4 \log ^2\left (-x+\frac {\sqrt [5]{\frac {1}{x}}}{-x+x^2}\right )} \]

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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[(E^(x^4*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2)*((-10*x^5 + 20*x^6 - 10*x^7 + (x^(-1))^(1/5)*(12*x
^3 - 22*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)] + (-20*x^5 + 40*x^6 - 20*x^7 + (x^(-1))^(1/5)*(-20*
x^3 + 20*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2))/(-5*x^2 + 10*x^3 - 5*x^4 + (x^(-1))^(1/5)*(-5
+ 5*x)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 3.31, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{x^4 \log ^2\left (\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2}\right )} \left (\left (-10 x^5+20 x^6-10 x^7+\sqrt [5]{\frac {1}{x}} \left (12 x^3-22 x^4\right )\right ) \log \left (\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2}\right )+\left (-20 x^5+40 x^6-20 x^7+\sqrt [5]{\frac {1}{x}} \left (-20 x^3+20 x^4\right )\right ) \log ^2\left (\frac {\sqrt [5]{\frac {1}{x}}+x^2-x^3}{-x+x^2}\right )\right )}{-5 x^2+10 x^3-5 x^4+\sqrt [5]{\frac {1}{x}} (-5+5 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^(x^4*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2)*((-10*x^5 + 20*x^6 - 10*x^7 + (x^(-1))^(1/5)
*(12*x^3 - 22*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)] + (-20*x^5 + 40*x^6 - 20*x^7 + (x^(-1))^(1/5)
*(-20*x^3 + 20*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2))/(-5*x^2 + 10*x^3 - 5*x^4 + (x^(-1))^(1/5
)*(-5 + 5*x)),x]

[Out]

Integrate[(E^(x^4*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2)*((-10*x^5 + 20*x^6 - 10*x^7 + (x^(-1))^(1/5)
*(12*x^3 - 22*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)] + (-20*x^5 + 40*x^6 - 20*x^7 + (x^(-1))^(1/5)
*(-20*x^3 + 20*x^4))*Log[((x^(-1))^(1/5) + x^2 - x^3)/(-x + x^2)]^2))/(-5*x^2 + 10*x^3 - 5*x^4 + (x^(-1))^(1/5
)*(-5 + 5*x)), x]

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fricas [A]  time = 0.61, size = 35, normalized size = 1.17 \begin {gather*} e^{\left (x^{4} \log \left (-\frac {x^{4} - x^{3} - x^{\frac {4}{5}}}{x^{3} - x^{2}}\right )^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((20*x^4-20*x^3)*(1/x)^(1/5)-20*x^7+40*x^6-20*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x))^2+((-22*x^4+1
2*x^3)*(1/x)^(1/5)-10*x^7+20*x^6-10*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x)))*exp(x^4*log(((1/x)^(1/5)-x^3+x^2)
/(x^2-x))^2)/((5*x-5)*(1/x)^(1/5)-5*x^4+10*x^3-5*x^2),x, algorithm="fricas")

[Out]

e^(x^4*log(-(x^4 - x^3 - x^(4/5))/(x^3 - x^2))^2)

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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((((20*x^4-20*x^3)*(1/x)^(1/5)-20*x^7+40*x^6-20*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x))^2+((-22*x^4+1
2*x^3)*(1/x)^(1/5)-10*x^7+20*x^6-10*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x)))*exp(x^4*log(((1/x)^(1/5)-x^3+x^2)
/(x^2-x))^2)/((5*x-5)*(1/x)^(1/5)-5*x^4+10*x^3-5*x^2),x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 0.09, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (20 x^{4}-20 x^{3}\right ) \left (\frac {1}{x}\right )^{\frac {1}{5}}-20 x^{7}+40 x^{6}-20 x^{5}\right ) \ln \left (\frac {\left (\frac {1}{x}\right )^{\frac {1}{5}}-x^{3}+x^{2}}{x^{2}-x}\right )^{2}+\left (\left (-22 x^{4}+12 x^{3}\right ) \left (\frac {1}{x}\right )^{\frac {1}{5}}-10 x^{7}+20 x^{6}-10 x^{5}\right ) \ln \left (\frac {\left (\frac {1}{x}\right )^{\frac {1}{5}}-x^{3}+x^{2}}{x^{2}-x}\right )\right ) {\mathrm e}^{x^{4} \ln \left (\frac {\left (\frac {1}{x}\right )^{\frac {1}{5}}-x^{3}+x^{2}}{x^{2}-x}\right )^{2}}}{\left (5 x -5\right ) \left (\frac {1}{x}\right )^{\frac {1}{5}}-5 x^{4}+10 x^{3}-5 x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((20*x^4-20*x^3)*(1/x)^(1/5)-20*x^7+40*x^6-20*x^5)*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x))^2+((-22*x^4+12*x^3)*
(1/x)^(1/5)-10*x^7+20*x^6-10*x^5)*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x)))*exp(x^4*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x))
^2)/((5*x-5)*(1/x)^(1/5)-5*x^4+10*x^3-5*x^2),x)

[Out]

int((((20*x^4-20*x^3)*(1/x)^(1/5)-20*x^7+40*x^6-20*x^5)*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x))^2+((-22*x^4+12*x^3)*
(1/x)^(1/5)-10*x^7+20*x^6-10*x^5)*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x)))*exp(x^4*ln(((1/x)^(1/5)-x^3+x^2)/(x^2-x))
^2)/((5*x-5)*(1/x)^(1/5)-5*x^4+10*x^3-5*x^2),x)

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maxima [B]  time = 1.07, size = 193, normalized size = 6.43 \begin {gather*} e^{\left (x^{4} \log \left (-x^{\frac {16}{5}} + x^{\frac {11}{5}} + 1\right )^{2} - \frac {12}{5} \, x^{4} \log \left (-x^{\frac {16}{5}} + x^{\frac {11}{5}} + 1\right ) \log \relax (x) + \frac {36}{25} \, x^{4} \log \relax (x)^{2} - 2 \, x^{4} \log \left (-x^{\frac {16}{5}} + x^{\frac {11}{5}} + 1\right ) \log \left (x^{\frac {4}{5}} + x^{\frac {3}{5}} + x^{\frac {2}{5}} + x^{\frac {1}{5}} + 1\right ) + \frac {12}{5} \, x^{4} \log \relax (x) \log \left (x^{\frac {4}{5}} + x^{\frac {3}{5}} + x^{\frac {2}{5}} + x^{\frac {1}{5}} + 1\right ) + x^{4} \log \left (x^{\frac {4}{5}} + x^{\frac {3}{5}} + x^{\frac {2}{5}} + x^{\frac {1}{5}} + 1\right )^{2} - 2 \, x^{4} \log \left (-x^{\frac {16}{5}} + x^{\frac {11}{5}} + 1\right ) \log \left (x^{\frac {1}{5}} - 1\right ) + \frac {12}{5} \, x^{4} \log \relax (x) \log \left (x^{\frac {1}{5}} - 1\right ) + 2 \, x^{4} \log \left (x^{\frac {4}{5}} + x^{\frac {3}{5}} + x^{\frac {2}{5}} + x^{\frac {1}{5}} + 1\right ) \log \left (x^{\frac {1}{5}} - 1\right ) + x^{4} \log \left (x^{\frac {1}{5}} - 1\right )^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((20*x^4-20*x^3)*(1/x)^(1/5)-20*x^7+40*x^6-20*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x))^2+((-22*x^4+1
2*x^3)*(1/x)^(1/5)-10*x^7+20*x^6-10*x^5)*log(((1/x)^(1/5)-x^3+x^2)/(x^2-x)))*exp(x^4*log(((1/x)^(1/5)-x^3+x^2)
/(x^2-x))^2)/((5*x-5)*(1/x)^(1/5)-5*x^4+10*x^3-5*x^2),x, algorithm="maxima")

[Out]

e^(x^4*log(-x^(16/5) + x^(11/5) + 1)^2 - 12/5*x^4*log(-x^(16/5) + x^(11/5) + 1)*log(x) + 36/25*x^4*log(x)^2 -
2*x^4*log(-x^(16/5) + x^(11/5) + 1)*log(x^(4/5) + x^(3/5) + x^(2/5) + x^(1/5) + 1) + 12/5*x^4*log(x)*log(x^(4/
5) + x^(3/5) + x^(2/5) + x^(1/5) + 1) + x^4*log(x^(4/5) + x^(3/5) + x^(2/5) + x^(1/5) + 1)^2 - 2*x^4*log(-x^(1
6/5) + x^(11/5) + 1)*log(x^(1/5) - 1) + 12/5*x^4*log(x)*log(x^(1/5) - 1) + 2*x^4*log(x^(4/5) + x^(3/5) + x^(2/
5) + x^(1/5) + 1)*log(x^(1/5) - 1) + x^4*log(x^(1/5) - 1)^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{x^4\,{\ln \left (-\frac {{\left (\frac {1}{x}\right )}^{1/5}+x^2-x^3}{x-x^2}\right )}^2}\,\left ({\ln \left (-\frac {{\left (\frac {1}{x}\right )}^{1/5}+x^2-x^3}{x-x^2}\right )}^2\,\left (\left (20\,x^3-20\,x^4\right )\,{\left (\frac {1}{x}\right )}^{1/5}+20\,x^5-40\,x^6+20\,x^7\right )-\ln \left (-\frac {{\left (\frac {1}{x}\right )}^{1/5}+x^2-x^3}{x-x^2}\right )\,\left (\left (12\,x^3-22\,x^4\right )\,{\left (\frac {1}{x}\right )}^{1/5}-10\,x^5+20\,x^6-10\,x^7\right )\right )}{\left (5\,x-5\right )\,{\left (\frac {1}{x}\right )}^{1/5}-5\,x^2+10\,x^3-5\,x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x^4*log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))^2)*(log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))^2*((20*x
^3 - 20*x^4)*(1/x)^(1/5) + 20*x^5 - 40*x^6 + 20*x^7) - log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))*((12*x^3 - 22
*x^4)*(1/x)^(1/5) - 10*x^5 + 20*x^6 - 10*x^7)))/((5*x - 5)*(1/x)^(1/5) - 5*x^2 + 10*x^3 - 5*x^4),x)

[Out]

int(-(exp(x^4*log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))^2)*(log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))^2*((20*x
^3 - 20*x^4)*(1/x)^(1/5) + 20*x^5 - 40*x^6 + 20*x^7) - log(-((1/x)^(1/5) + x^2 - x^3)/(x - x^2))*((12*x^3 - 22
*x^4)*(1/x)^(1/5) - 10*x^5 + 20*x^6 - 10*x^7)))/((5*x - 5)*(1/x)^(1/5) - 5*x^2 + 10*x^3 - 5*x^4), x)

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sympy [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((((20*x**4-20*x**3)*(1/x)**(1/5)-20*x**7+40*x**6-20*x**5)*ln(((1/x)**(1/5)-x**3+x**2)/(x**2-x))**2+(
(-22*x**4+12*x**3)*(1/x)**(1/5)-10*x**7+20*x**6-10*x**5)*ln(((1/x)**(1/5)-x**3+x**2)/(x**2-x)))*exp(x**4*ln(((
1/x)**(1/5)-x**3+x**2)/(x**2-x))**2)/((5*x-5)*(1/x)**(1/5)-5*x**4+10*x**3-5*x**2),x)

[Out]

Timed out

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