3.47.20 \(\int \frac {-5 e+5 e^{e^5 x^2+x^3}+5 x+(5 e-10 x+e^{e^5 x^2+x^3} (-5-10 e^5 x^2-15 x^3)) \log (x)}{e^2 x^2+e^{2 e^5 x^2+2 x^3} x^2-2 e x^3+x^4+e^{e^5 x^2+x^3} (-2 e x^2+2 x^3)} \, dx\)

Optimal. Leaf size=25 \[ \frac {5 \log (x)}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \]

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Rubi [F]  time = 3.43, 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 {-5 e+5 e^{e^5 x^2+x^3}+5 x+\left (5 e-10 x+e^{e^5 x^2+x^3} \left (-5-10 e^5 x^2-15 x^3\right )\right ) \log (x)}{e^2 x^2+e^{2 e^5 x^2+2 x^3} x^2-2 e x^3+x^4+e^{e^5 x^2+x^3} \left (-2 e x^2+2 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-5*E + 5*E^(E^5*x^2 + x^3) + 5*x + (5*E - 10*x + E^(E^5*x^2 + x^3)*(-5 - 10*E^5*x^2 - 15*x^3))*Log[x])/(E
^2*x^2 + E^(2*E^5*x^2 + 2*x^3)*x^2 - 2*E*x^3 + x^4 + E^(E^5*x^2 + x^3)*(-2*E*x^2 + 2*x^3)),x]

[Out]

-10*Log[x]*Defer[Int][E^(5 + E^5*x^2 + x^3)/(E - E^(x^2*(E^5 + x)) - x)^2, x] - 15*E*Log[x]*Defer[Int][x/(E -
E^(x^2*(E^5 + x)) - x)^2, x] - 5*Log[x]*Defer[Int][1/(x*(-E + E^(x^2*(E^5 + x)) + x)^2), x] + 15*Log[x]*Defer[
Int][x^2/(-E + E^(x^2*(E^5 + x)) + x)^2, x] + 5*Defer[Int][1/(x^2*(-E + E^(x^2*(E^5 + x)) + x)), x] - 5*Log[x]
*Defer[Int][1/(x^2*(-E + E^(x^2*(E^5 + x)) + x)), x] - 15*Log[x]*Defer[Int][x/(-E + E^(x^2*(E^5 + x)) + x), x]
+ 10*Defer[Int][Defer[Int][E^(5 + E^5*x^2 + x^3)/(-E + E^(x^2*(E^5 + x)) + x)^2, x]/x, x] + 5*Defer[Int][Defe
r[Int][1/(x*(-E + E^(x^2*(E^5 + x)) + x)^2), x]/x, x] + 15*E*Defer[Int][Defer[Int][x/(-E + E^(x^2*(E^5 + x)) +
x)^2, x]/x, x] - 15*Defer[Int][Defer[Int][x^2/(-E + E^(x^2*(E^5 + x)) + x)^2, x]/x, x] + 5*Defer[Int][Defer[I
nt][1/(x^2*(-E + E^(x^2*(E^5 + x)) + x)), x]/x, x] + 15*Defer[Int][Defer[Int][x/(-E + E^(x^2*(E^5 + x)) + x),
x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \left (-e+e^{x^2 \left (e^5+x\right )}+x-\left (-e+2 x+2 e^{5+e^5 x^2+x^3} x^2+e^{x^2 \left (e^5+x\right )} \left (1+3 x^3\right )\right ) \log (x)\right )}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2 x^2} \, dx\\ &=5 \int \frac {-e+e^{x^2 \left (e^5+x\right )}+x-\left (-e+2 x+2 e^{5+e^5 x^2+x^3} x^2+e^{x^2 \left (e^5+x\right )} \left (1+3 x^3\right )\right ) \log (x)}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2 x^2} \, dx\\ &=5 \int \left (\frac {\left (-1-2 e^{5+e^5 x^2+x^3} x-3 e x^2+3 x^3\right ) \log (x)}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2}-\frac {-1+\log (x)+3 x^3 \log (x)}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )}\right ) \, dx\\ &=5 \int \frac {\left (-1-2 e^{5+e^5 x^2+x^3} x-3 e x^2+3 x^3\right ) \log (x)}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-5 \int \frac {-1+\log (x)+3 x^3 \log (x)}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx\\ &=-\left (5 \int \left (-\frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )}+\frac {\log (x)}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )}+\frac {3 x \log (x)}{-e+e^{x^2 \left (e^5+x\right )}+x}\right ) \, dx\right )-5 \int \frac {-2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-3 e \int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx+3 \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \frac {\log (x)}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \left (\frac {-2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-3 e \int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}+\frac {3 \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}\right ) \, dx-15 \int \frac {x \log (x)}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \frac {-2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-3 e \int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+5 \int \frac {\int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx}{x} \, dx-15 \int \frac {\int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(5 \log (x)) \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 \log (x)) \int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \left (\frac {-2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}-\frac {3 e \int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}\right ) \, dx+5 \int \frac {\int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx}{x} \, dx-15 \int \frac {\int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(5 \log (x)) \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 \log (x)) \int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \frac {-2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+5 \int \frac {\int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx}{x} \, dx-15 \int \frac {\int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx}{x} \, dx+(15 e) \int \frac {\int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(5 \log (x)) \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 \log (x)) \int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-5 \int \left (-\frac {2 \int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}-\frac {\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x}\right ) \, dx+5 \int \frac {\int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx}{x} \, dx-15 \int \frac {\int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx}{x} \, dx+(15 e) \int \frac {\int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(5 \log (x)) \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 \log (x)) \int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ &=5 \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx+5 \int \frac {\int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+5 \int \frac {\int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx}{x} \, dx+10 \int \frac {\int \frac {e^{5+e^5 x^2+x^3}}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx-15 \int \frac {\int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx+15 \int \frac {\int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx}{x} \, dx+(15 e) \int \frac {\int \frac {x}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx}{x} \, dx-(5 \log (x)) \int \frac {1}{x \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(5 \log (x)) \int \frac {1}{x^2 \left (-e+e^{x^2 \left (e^5+x\right )}+x\right )} \, dx-(10 \log (x)) \int \frac {e^{5+e^5 x^2+x^3}}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx+(15 \log (x)) \int \frac {x^2}{\left (-e+e^{x^2 \left (e^5+x\right )}+x\right )^2} \, dx-(15 \log (x)) \int \frac {x}{-e+e^{x^2 \left (e^5+x\right )}+x} \, dx-(15 e \log (x)) \int \frac {x}{\left (e-e^{x^2 \left (e^5+x\right )}-x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 27, normalized size = 1.08 \begin {gather*} \frac {5 \log (x)}{x \left (-e+e^{e^5 x^2+x^3}+x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-5*E + 5*E^(E^5*x^2 + x^3) + 5*x + (5*E - 10*x + E^(E^5*x^2 + x^3)*(-5 - 10*E^5*x^2 - 15*x^3))*Log[
x])/(E^2*x^2 + E^(2*E^5*x^2 + 2*x^3)*x^2 - 2*E*x^3 + x^4 + E^(E^5*x^2 + x^3)*(-2*E*x^2 + 2*x^3)),x]

[Out]

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

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fricas [A]  time = 0.72, size = 28, normalized size = 1.12 \begin {gather*} \frac {5 \, \log \relax (x)}{x^{2} - x e + x e^{\left (x^{3} + x^{2} e^{5}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-10*x^2*exp(5)-15*x^3-5)*exp(x^2*exp(5)+x^3)+5*exp(1)-10*x)*log(x)+5*exp(x^2*exp(5)+x^3)-5*exp(1)
+5*x)/(x^2*exp(x^2*exp(5)+x^3)^2+(-2*x^2*exp(1)+2*x^3)*exp(x^2*exp(5)+x^3)+x^2*exp(1)^2-2*x^3*exp(1)+x^4),x, a
lgorithm="fricas")

[Out]

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

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giac [B]  time = 0.30, size = 172, normalized size = 6.88 \begin {gather*} \frac {5 \, {\left (3 \, x^{3} \log \relax (x) + 2 \, x^{2} e^{5} \log \relax (x) - 3 \, x^{2} e \log \relax (x) - 2 \, x e^{6} \log \relax (x) - \log \relax (x)\right )}}{3 \, x^{5} + 2 \, x^{4} e^{5} - 6 \, x^{4} e + 3 \, x^{4} e^{\left (x^{3} + x^{2} e^{5}\right )} - 4 \, x^{3} e^{6} + 3 \, x^{3} e^{2} + 2 \, x^{3} e^{\left (x^{3} + x^{2} e^{5} + 5\right )} - 3 \, x^{3} e^{\left (x^{3} + x^{2} e^{5} + 1\right )} + 2 \, x^{2} e^{7} - 2 \, x^{2} e^{\left (x^{3} + x^{2} e^{5} + 6\right )} - x^{2} + x e - x e^{\left (x^{3} + x^{2} e^{5}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-10*x^2*exp(5)-15*x^3-5)*exp(x^2*exp(5)+x^3)+5*exp(1)-10*x)*log(x)+5*exp(x^2*exp(5)+x^3)-5*exp(1)
+5*x)/(x^2*exp(x^2*exp(5)+x^3)^2+(-2*x^2*exp(1)+2*x^3)*exp(x^2*exp(5)+x^3)+x^2*exp(1)^2-2*x^3*exp(1)+x^4),x, a
lgorithm="giac")

[Out]

5*(3*x^3*log(x) + 2*x^2*e^5*log(x) - 3*x^2*e*log(x) - 2*x*e^6*log(x) - log(x))/(3*x^5 + 2*x^4*e^5 - 6*x^4*e +
3*x^4*e^(x^3 + x^2*e^5) - 4*x^3*e^6 + 3*x^3*e^2 + 2*x^3*e^(x^3 + x^2*e^5 + 5) - 3*x^3*e^(x^3 + x^2*e^5 + 1) +
2*x^2*e^7 - 2*x^2*e^(x^3 + x^2*e^5 + 6) - x^2 + x*e - x*e^(x^3 + x^2*e^5))

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maple [A]  time = 0.05, size = 27, normalized size = 1.08

method	result	size
risch	\(-\frac {5 \ln \relax (x )}{x \left ({\mathrm e}-x -{\mathrm e}^{x^{2} \left ({\mathrm e}^{5}+x \right )}\right )}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-10*x^2*exp(5)-15*x^3-5)*exp(x^2*exp(5)+x^3)+5*exp(1)-10*x)*ln(x)+5*exp(x^2*exp(5)+x^3)-5*exp(1)+5*x)/(
x^2*exp(x^2*exp(5)+x^3)^2+(-2*x^2*exp(1)+2*x^3)*exp(x^2*exp(5)+x^3)+x^2*exp(1)^2-2*x^3*exp(1)+x^4),x,method=_R
ETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.42, size = 28, normalized size = 1.12 \begin {gather*} \frac {5 \, \log \relax (x)}{x^{2} - x e + x e^{\left (x^{3} + x^{2} e^{5}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-10*x^2*exp(5)-15*x^3-5)*exp(x^2*exp(5)+x^3)+5*exp(1)-10*x)*log(x)+5*exp(x^2*exp(5)+x^3)-5*exp(1)
+5*x)/(x^2*exp(x^2*exp(5)+x^3)^2+(-2*x^2*exp(1)+2*x^3)*exp(x^2*exp(5)+x^3)+x^2*exp(1)^2-2*x^3*exp(1)+x^4),x, a
lgorithm="maxima")

[Out]

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

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mupad [B]  time = 3.71, size = 90, normalized size = 3.60 \begin {gather*} \frac {5\,x\,\ln \relax (x)-15\,x^4\,\ln \relax (x)+x^3\,\left (15\,\mathrm {e}\,\ln \relax (x)-10\,{\mathrm {e}}^5\,\ln \relax (x)\right )+10\,x^2\,{\mathrm {e}}^6\,\ln \relax (x)}{x^2\,\left (x+{\mathrm {e}}^{x^3+{\mathrm {e}}^5\,x^2}-\mathrm {e}\right )\,\left (2\,x\,{\mathrm {e}}^6+3\,x^2\,\mathrm {e}-2\,x^2\,{\mathrm {e}}^5-3\,x^3+1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*x + 5*exp(x^2*exp(5) + x^3) - 5*exp(1) - log(x)*(10*x - 5*exp(1) + exp(x^2*exp(5) + x^3)*(10*x^2*exp(5)
+ 15*x^3 + 5)))/(x^2*exp(2) - 2*x^3*exp(1) - exp(x^2*exp(5) + x^3)*(2*x^2*exp(1) - 2*x^3) + x^2*exp(2*x^2*exp
(5) + 2*x^3) + x^4),x)

[Out]

(5*x*log(x) - 15*x^4*log(x) + x^3*(15*exp(1)*log(x) - 10*exp(5)*log(x)) + 10*x^2*exp(6)*log(x))/(x^2*(x + exp(
x^2*exp(5) + x^3) - exp(1))*(2*x*exp(6) + 3*x^2*exp(1) - 2*x^2*exp(5) - 3*x^3 + 1))

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sympy [A]  time = 0.31, size = 26, normalized size = 1.04 \begin {gather*} \frac {5 \log {\relax (x )}}{x^{2} + x e^{x^{3} + x^{2} e^{5}} - e x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-10*x**2*exp(5)-15*x**3-5)*exp(x**2*exp(5)+x**3)+5*exp(1)-10*x)*ln(x)+5*exp(x**2*exp(5)+x**3)-5*e
xp(1)+5*x)/(x**2*exp(x**2*exp(5)+x**3)**2+(-2*x**2*exp(1)+2*x**3)*exp(x**2*exp(5)+x**3)+x**2*exp(1)**2-2*x**3*
exp(1)+x**4),x)

[Out]

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

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