3.93.69 \(\int \frac {3 x+e^{e^5+x^2} (36-24 x^2)+e^{x^2} (36 x-24 x^3)+(e^{e^5+x^2} (-9+6 x^2)+e^{x^2} (-9 x+6 x^3)) \log (e^{e^5}+x)+(36 e^{e^5}+36 x+(-9 e^{e^5}-9 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(12 e^{e^5+x^2}+12 e^{x^2} x+(-3 e^{e^5+x^2}-3 e^{x^2} x) \log (e^{e^5}+x)+(12 e^{e^5}+12 x+(-3 e^{e^5}-3 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})+(-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+(e^{e^5+x^2} x^2+e^{x^2} x^3) \log (e^{e^5}+x)+(-4 e^{e^5} x^2-4 x^3+(e^{e^5} x^2+x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log ^2(\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})} \, dx\)
Optimal. Leaf size=31 \[ \frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \]
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Rubi [A] time = 4.89, antiderivative size = 31, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 3, integrand size = 618, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used
= {6688, 12, 6687} \begin {gather*} \frac {3}{x \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^(E^5 + x^2)*(-9 + 6*x^2) + E^x^2*(-9*x + 6
*x^3))*Log[E^E^5 + x] + (36*E^E^5 + 36*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (12*E^(
E^5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x] + (12*E^E^5 + 12*x + (-3*E^E^5 - 3*x)*
Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*x^2 -
16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4
*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2
+ 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E
^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 + x^2)*x
^2 + E^x^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5
+ x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]^2),x]
[Out]
3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 6687
Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y*z, u*z^(n - m), x]}, Simp[(q*y^(m +
1)*z^(m + 1))/(m + 1), x] /; !FalseQ[q]] /; FreeQ[{m, n}, x] && NeQ[m, -1]
Rule 6688
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-12 e^{e^5+x^2}-x-12 e^{x^2} x+8 e^{e^5+x^2} x^2+8 e^{x^2} x^3-4 e^{e^5+x^2} \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 e^{x^2} x \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 \left (e^{e^5}+x\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\left (e^{e^5}+x\right ) \log \left (e^{e^5}+x\right ) \left (e^{x^2} \left (-3+2 x^2-\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )\right )\right )}{x^2 \left (e^{e^5}+x\right ) \left (4-\log \left (e^{e^5}+x\right )\right ) \left (e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )^2} \, dx\\ &=3 \int \frac {-12 e^{e^5+x^2}-x-12 e^{x^2} x+8 e^{e^5+x^2} x^2+8 e^{x^2} x^3-4 e^{e^5+x^2} \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 e^{x^2} x \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )-4 \left (e^{e^5}+x\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\left (e^{e^5}+x\right ) \log \left (e^{e^5}+x\right ) \left (e^{x^2} \left (-3+2 x^2-\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )-\log \left (-4+\log \left (e^{e^5}+x\right )\right ) \left (3+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )\right )}{x^2 \left (e^{e^5}+x\right ) \left (4-\log \left (e^{e^5}+x\right )\right ) \left (e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )^2} \, dx\\ &=\frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.62, size = 31, normalized size = 1.00 \begin {gather*} \frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^(E^5 + x^2)*(-9 + 6*x^2) + E^x^2*(-9
*x + 6*x^3))*Log[E^E^5 + x] + (36*E^E^5 + 36*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (
12*E^(E^5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x] + (12*E^E^5 + 12*x + (-3*E^E^5 -
3*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*
x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x
^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2
)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 +
Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 +
x^2)*x^2 + E^x^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*Log[E^E^5 + x])*Log[-4 + Log[
E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]^2),x]
[Out]
3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))
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fricas [A] time = 0.76, size = 39, normalized size = 1.26 \begin {gather*} \frac {3}{x \log \left (\frac {x e^{\left (e^{5}\right )}}{e^{\left (e^{5}\right )} \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right ) + e^{\left (x^{2} + e^{5}\right )}}\right ) + 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="fricas")
[Out]
3/(x*log(x*e^(e^5)/(e^(e^5)*log(log(x + e^(e^5)) - 4) + e^(x^2 + e^5))) + 2*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(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="giac")
[Out]
Timed out
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maple [C] time = 0.32, size = 185, normalized size = 5.97
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\(\frac {6 i}{x \left (\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )^{3}+2 i \ln \relax (x )-2 i \ln \left (\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}\right )+4 i\right )}\) |
\(185\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*ln(ln(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(ex
p(5))-3*exp(x^2)*x)*ln(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp
(x^2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36*x)*ln(ln(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^
2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*ln(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3+36*x)*exp(x^
2)+3*x)/((((x^2*exp(exp(5))+x^3)*ln(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*ln(ln(exp(exp(5))+x)-4)+(x^2*exp(x
^2)*exp(exp(5))+x^3*exp(x^2))*ln(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*ln(x/(ln(ln(exp(exp
(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*ln(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*ln(ln(exp(exp
(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*ex
p(x^2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*ln(exp(exp(5))+x)-16*x^2*exp(exp(5
))-16*x^3)*ln(ln(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^
2)*exp(exp(5))-16*x^3*exp(x^2)),x,method=_RETURNVERBOSE)
[Out]
6*I/x/(Pi*csgn(I*x)*csgn(I/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))-Pi
*csgn(I*x)*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^2-Pi*csgn(I/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I
*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^2+Pi*csgn(I*x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^3+2*I*ln(x)-2*I*ln(ln
(ln(exp(exp(5))+x)-4)+exp(x^2))+4*I)
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maxima [A] time = 0.67, size = 30, normalized size = 0.97 \begin {gather*} \frac {3}{x \log \relax (x) - x \log \left (e^{\left (x^{2}\right )} + \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right )\right ) + 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(log(exp(exp(5))+x)-4)+(-3*exp(x^
2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(
5))+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x)*log(log(exp(exp(5))+x)-4)+(
(6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24
*x^3+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*log(log(exp(exp(
5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2)
)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(
5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*ex
p(x^2)*exp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*log
(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2
))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="maxima")
[Out]
3/(x*log(x) - x*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + 2*x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {3\,x+\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )\,\left (12\,x\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}+3\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+12\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (12\,x+12\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (3\,x+3\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )\right )\right )+{\mathrm {e}}^{x^2}\,\left (36\,x-24\,x^3\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (36\,x+36\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (9\,x+9\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )\right )-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left ({\mathrm {e}}^{x^2}\,\left (9\,x-6\,x^3\right )-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,\left (6\,x^2-9\right )\right )-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,\left (24\,x^2-36\right )}{16\,x^3\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (16\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3+4\,{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+16\,x^3\right )+\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )\,\left (16\,x^3\,{\mathrm {e}}^{x^2}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (16\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (4\,x^3+4\,{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+16\,x^3\right )+16\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+{\ln \left (\frac {x}{{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )}\right )}^2\,\left (4\,x^3\,{\mathrm {e}}^{x^2}+\ln \left (\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )-4\right )\,\left (4\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^5}-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (x^3+{\mathrm {e}}^{{\mathrm {e}}^5}\,x^2\right )+4\,x^3\right )-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^5}\right )\,\left (x^3\,{\mathrm {e}}^{x^2}+x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+4\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}\right )+16\,x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^5}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^2) - log(x + exp(exp(5)))*(3*x*exp(x
^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5))
- log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + log(log(x + exp(exp(5))) - 4)*(36
*x + 36*exp(exp(5)) - log(x + exp(exp(5)))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^
3) - exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/(16*x^3*exp(x^2) - log(x + exp(ex
p(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log
(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(1
6*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5)))
- 4)*(16*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + 16*x^2*exp(x^2)*exp(e
xp(5))) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*
(4*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + exp(exp(5)))*(x^3*exp(x^2
) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*exp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))),x)
[Out]
int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^2) - log(x + exp(exp(5)))*(3*x*exp(x
^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5))
- log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + log(log(x + exp(exp(5))) - 4)*(36
*x + 36*exp(exp(5)) - log(x + exp(exp(5)))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^
3) - exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/(16*x^3*exp(x^2) - log(x + exp(ex
p(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log
(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(1
6*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5)))
- 4)*(16*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + 16*x^2*exp(x^2)*exp(e
xp(5))) + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*
(4*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + exp(exp(5)))*(x^3*exp(x^2
) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*exp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))), 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(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*ln(ln(exp(exp(5))+x)-4)+(-3*exp(x**2)
*exp(exp(5))-3*exp(x**2)*x)*ln(exp(exp(5))+x)+12*exp(x**2)*exp(exp(5))+12*exp(x**2)*x)*ln(x/(ln(ln(exp(exp(5))
+x)-4)+exp(x**2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36*x)*ln(ln(exp(exp(5))+x)-4)+((6*x*
*2-9)*exp(x**2)*exp(exp(5))+(6*x**3-9*x)*exp(x**2))*ln(exp(exp(5))+x)+(-24*x**2+36)*exp(x**2)*exp(exp(5))+(-24
*x**3+36*x)*exp(x**2)+3*x)/((((x**2*exp(exp(5))+x**3)*ln(exp(exp(5))+x)-4*x**2*exp(exp(5))-4*x**3)*ln(ln(exp(e
xp(5))+x)-4)+(x**2*exp(x**2)*exp(exp(5))+x**3*exp(x**2))*ln(exp(exp(5))+x)-4*x**2*exp(x**2)*exp(exp(5))-4*x**3
*exp(x**2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x**2)))**2+(((4*x**2*exp(exp(5))+4*x**3)*ln(exp(exp(5))+x)-16*x*
*2*exp(exp(5))-16*x**3)*ln(ln(exp(exp(5))+x)-4)+(4*x**2*exp(x**2)*exp(exp(5))+4*x**3*exp(x**2))*ln(exp(exp(5))
+x)-16*x**2*exp(x**2)*exp(exp(5))-16*x**3*exp(x**2))*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x**2)))+((4*x**2*exp(ex
p(5))+4*x**3)*ln(exp(exp(5))+x)-16*x**2*exp(exp(5))-16*x**3)*ln(ln(exp(exp(5))+x)-4)+(4*x**2*exp(x**2)*exp(exp
(5))+4*x**3*exp(x**2))*ln(exp(exp(5))+x)-16*x**2*exp(x**2)*exp(exp(5))-16*x**3*exp(x**2)),x)
[Out]
Timed out
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