3.18.74 \(\int \frac {-x^3 \log (x)+x^3 \log ^2(x)+(-3 x^2 \log (x)+3 x^2 \log ^2(x)) \log (\log (x))+(-3 x \log (x)+3 x \log ^2(x)) \log ^2(\log (x))+(-\log (x)+\log ^2(x)) \log ^3(\log (x))+e^{\frac {x^2+2 x^3+x^4+(2 x^2+2 x^3) \log (\log (x))+x^2 \log ^2(\log (x))}{x^2+2 x \log (\log (x))+\log ^2(\log (x))}} (2 x^2+2 x^3+(x^3-2 x^4-2 x^5) \log (x)+(2 x^2+(x^2-6 x^3-6 x^4) \log (x)) \log (\log (x))+(3 x-4 x^2-6 x^3) \log (x) \log ^2(\log (x))+(1-2 x^2) \log (x) \log ^3(\log (x)))}{x^4 \log ^2(x)+3 x^3 \log ^2(x) \log (\log (x))+3 x^2 \log ^2(x) \log ^2(\log (x))+x \log ^2(x) \log ^3(\log (x))+e^{\frac {x^2+2 x^3+x^4+(2 x^2+2 x^3) \log (\log (x))+x^2 \log ^2(\log (x))}{x^2+2 x \log (\log (x))+\log ^2(\log (x))}} (x^4 \log (x)+3 x^3 \log (x) \log (\log (x))+3 x^2 \log (x) \log ^2(\log (x))+x \log (x) \log ^3(\log (x)))} \, dx\)

Optimal. Leaf size=23 \[ \log \left (\frac {x}{e^{\left (x+\frac {x}{x+\log (\log (x))}\right )^2}+\log (x)}\right ) \]

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Rubi [F]  time = 25.97, 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 {-x^3 \log (x)+x^3 \log ^2(x)+\left (-3 x^2 \log (x)+3 x^2 \log ^2(x)\right ) \log (\log (x))+\left (-3 x \log (x)+3 x \log ^2(x)\right ) \log ^2(\log (x))+\left (-\log (x)+\log ^2(x)\right ) \log ^3(\log (x))+\exp \left (\frac {x^2+2 x^3+x^4+\left (2 x^2+2 x^3\right ) \log (\log (x))+x^2 \log ^2(\log (x))}{x^2+2 x \log (\log (x))+\log ^2(\log (x))}\right ) \left (2 x^2+2 x^3+\left (x^3-2 x^4-2 x^5\right ) \log (x)+\left (2 x^2+\left (x^2-6 x^3-6 x^4\right ) \log (x)\right ) \log (\log (x))+\left (3 x-4 x^2-6 x^3\right ) \log (x) \log ^2(\log (x))+\left (1-2 x^2\right ) \log (x) \log ^3(\log (x))\right )}{x^4 \log ^2(x)+3 x^3 \log ^2(x) \log (\log (x))+3 x^2 \log ^2(x) \log ^2(\log (x))+x \log ^2(x) \log ^3(\log (x))+\exp \left (\frac {x^2+2 x^3+x^4+\left (2 x^2+2 x^3\right ) \log (\log (x))+x^2 \log ^2(\log (x))}{x^2+2 x \log (\log (x))+\log ^2(\log (x))}\right ) \left (x^4 \log (x)+3 x^3 \log (x) \log (\log (x))+3 x^2 \log (x) \log ^2(\log (x))+x \log (x) \log ^3(\log (x))\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-(x^3*Log[x]) + x^3*Log[x]^2 + (-3*x^2*Log[x] + 3*x^2*Log[x]^2)*Log[Log[x]] + (-3*x*Log[x] + 3*x*Log[x]^2
)*Log[Log[x]]^2 + (-Log[x] + Log[x]^2)*Log[Log[x]]^3 + E^((x^2 + 2*x^3 + x^4 + (2*x^2 + 2*x^3)*Log[Log[x]] + x
^2*Log[Log[x]]^2)/(x^2 + 2*x*Log[Log[x]] + Log[Log[x]]^2))*(2*x^2 + 2*x^3 + (x^3 - 2*x^4 - 2*x^5)*Log[x] + (2*
x^2 + (x^2 - 6*x^3 - 6*x^4)*Log[x])*Log[Log[x]] + (3*x - 4*x^2 - 6*x^3)*Log[x]*Log[Log[x]]^2 + (1 - 2*x^2)*Log
[x]*Log[Log[x]]^3))/(x^4*Log[x]^2 + 3*x^3*Log[x]^2*Log[Log[x]] + 3*x^2*Log[x]^2*Log[Log[x]]^2 + x*Log[x]^2*Log
[Log[x]]^3 + E^((x^2 + 2*x^3 + x^4 + (2*x^2 + 2*x^3)*Log[Log[x]] + x^2*Log[Log[x]]^2)/(x^2 + 2*x*Log[Log[x]] +
Log[Log[x]]^2))*(x^4*Log[x] + 3*x^3*Log[x]*Log[Log[x]] + 3*x^2*Log[x]*Log[Log[x]]^2 + x*Log[x]*Log[Log[x]]^3)
),x]

[Out]

-x^2 + Log[x] + 2*Defer[Int][x^2/(x + Log[Log[x]])^3, x] + 2*Defer[Int][x/(Log[x]*(x + Log[Log[x]])^3), x] - 2
*Defer[Int][x/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] - 3*D
efer[Int][x^2/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] + 2*D
efer[Int][(x^3*Log[x])/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3),
x] + 2*Defer[Int][(x^4*Log[x])/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log
[x]])^3), x] - 5*Defer[Int][(x*Log[Log[x]])/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*
(x + Log[Log[x]])^3), x] + 2*Defer[Int][(x*Log[x]*Log[Log[x]])/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log
[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] + 6*Defer[Int][(x^2*Log[x]*Log[Log[x]])/((E^((x^2*(1 + x + Log[Log
[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] + 6*Defer[Int][(x^3*Log[x]*Log[Log[x]])/((E^(
(x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] - 3*Defer[Int][Log[Log[x
]]^2/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] + 4*Defer[Int]
[(x*Log[x]*Log[Log[x]]^2)/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^
3), x] + 6*Defer[Int][(x^2*Log[x]*Log[Log[x]]^2)/((E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]])^2) + Log
[x])*(x + Log[Log[x]])^3), x] - Defer[Int][Log[Log[x]]^3/(x*(E^((x^2*(1 + x + Log[Log[x]])^2)/(x + Log[Log[x]]
)^2) + Log[x])*(x + Log[Log[x]])^3), x] + 2*Defer[Int][(x*Log[x]*Log[Log[x]]^3)/((E^((x^2*(1 + x + Log[Log[x]]
)^2)/(x + Log[Log[x]])^2) + Log[x])*(x + Log[Log[x]])^3), x] - 2*Defer[Int][x/(x + Log[Log[x]])^2, x] + 2*Defe
r[Int][x^2/(x + Log[Log[x]])^2, x] + 2*Defer[Int][x/(Log[x]*(x + Log[Log[x]])^2), x] - 4*Defer[Int][x/(x + Log
[Log[x]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x^3 \log (x)+x^3 \log ^2(x)+3 x^2 (-1+\log (x)) \log (x) \log (\log (x))+3 x (-1+\log (x)) \log (x) \log ^2(\log (x))+(-1+\log (x)) \log (x) \log ^3(\log (x))+\exp \left (\frac {x^2 (1+x+\log (\log (x)))^2}{(x+\log (\log (x)))^2}\right ) \left (2 x^2 (1+x+\log (\log (x)))+\log (x) \left (x^3-2 x^4-2 x^5+\left (x^2-6 x^3-6 x^4\right ) \log (\log (x))+x \left (3-4 x-6 x^2\right ) \log ^2(\log (x))+\left (1-2 x^2\right ) \log ^3(\log (x))\right )\right )}{x \log (x) \left (\exp \left (\frac {x^2 (1+x+\log (\log (x)))^2}{(x+\log (\log (x)))^2}\right )+\log (x)\right ) (x+\log (\log (x)))^3} \, dx\\ &=\int \left (\frac {2 x^2+2 x^3+x^3 \log (x)-2 x^4 \log (x)-2 x^5 \log (x)+2 x^2 \log (\log (x))+x^2 \log (x) \log (\log (x))-6 x^3 \log (x) \log (\log (x))-6 x^4 \log (x) \log (\log (x))+3 x \log (x) \log ^2(\log (x))-4 x^2 \log (x) \log ^2(\log (x))-6 x^3 \log (x) \log ^2(\log (x))+\log (x) \log ^3(\log (x))-2 x^2 \log (x) \log ^3(\log (x))}{x \log (x) (x+\log (\log (x)))^3}+\frac {-2 x^2-3 x^3+2 x^4 \log (x)+2 x^5 \log (x)-5 x^2 \log (\log (x))+2 x^2 \log (x) \log (\log (x))+6 x^3 \log (x) \log (\log (x))+6 x^4 \log (x) \log (\log (x))-3 x \log ^2(\log (x))+4 x^2 \log (x) \log ^2(\log (x))+6 x^3 \log (x) \log ^2(\log (x))-\log ^3(\log (x))+2 x^2 \log (x) \log ^3(\log (x))}{x \left (\exp \left (\frac {x^2 (1+x+\log (\log (x)))^2}{(x+\log (\log (x)))^2}\right )+\log (x)\right ) (x+\log (\log (x)))^3}\right ) \, dx\\ &=\int \frac {2 x^2+2 x^3+x^3 \log (x)-2 x^4 \log (x)-2 x^5 \log (x)+2 x^2 \log (\log (x))+x^2 \log (x) \log (\log (x))-6 x^3 \log (x) \log (\log (x))-6 x^4 \log (x) \log (\log (x))+3 x \log (x) \log ^2(\log (x))-4 x^2 \log (x) \log ^2(\log (x))-6 x^3 \log (x) \log ^2(\log (x))+\log (x) \log ^3(\log (x))-2 x^2 \log (x) \log ^3(\log (x))}{x \log (x) (x+\log (\log (x)))^3} \, dx+\int \frac {-2 x^2-3 x^3+2 x^4 \log (x)+2 x^5 \log (x)-5 x^2 \log (\log (x))+2 x^2 \log (x) \log (\log (x))+6 x^3 \log (x) \log (\log (x))+6 x^4 \log (x) \log (\log (x))-3 x \log ^2(\log (x))+4 x^2 \log (x) \log ^2(\log (x))+6 x^3 \log (x) \log ^2(\log (x))-\log ^3(\log (x))+2 x^2 \log (x) \log ^3(\log (x))}{x \left (\exp \left (\frac {x^2 (1+x+\log (\log (x)))^2}{(x+\log (\log (x)))^2}\right )+\log (x)\right ) (x+\log (\log (x)))^3} \, dx\\ &=\int \frac {-x^2 (2+3 x)-5 x^2 \log (\log (x))-3 x \log ^2(\log (x))-\log ^3(\log (x))+2 x^2 \log (x) \left (x^2 (1+x)+\left (1+3 x+3 x^2\right ) \log (\log (x))+(2+3 x) \log ^2(\log (x))+\log ^3(\log (x))\right )}{x \left (\exp \left (\frac {x^2 (1+x+\log (\log (x)))^2}{(x+\log (\log (x)))^2}\right )+\log (x)\right ) (x+\log (\log (x)))^3} \, dx+\int \frac {2 x^2 (1+x+\log (\log (x)))+\log (x) \left (x^3-2 x^4-2 x^5+\left (x^2-6 x^3-6 x^4\right ) \log (\log (x))+x \left (3-4 x-6 x^2\right ) \log ^2(\log (x))+\left (1-2 x^2\right ) \log ^3(\log (x))\right )}{x \log (x) (x+\log (\log (x)))^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.39, size = 38, normalized size = 1.65 \begin {gather*} \log (x)-\log \left (e^{x^2+\frac {x^2}{(x+\log (\log (x)))^2}+\frac {2 x^2}{x+\log (\log (x))}}+\log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-(x^3*Log[x]) + x^3*Log[x]^2 + (-3*x^2*Log[x] + 3*x^2*Log[x]^2)*Log[Log[x]] + (-3*x*Log[x] + 3*x*Lo
g[x]^2)*Log[Log[x]]^2 + (-Log[x] + Log[x]^2)*Log[Log[x]]^3 + E^((x^2 + 2*x^3 + x^4 + (2*x^2 + 2*x^3)*Log[Log[x
]] + x^2*Log[Log[x]]^2)/(x^2 + 2*x*Log[Log[x]] + Log[Log[x]]^2))*(2*x^2 + 2*x^3 + (x^3 - 2*x^4 - 2*x^5)*Log[x]
+ (2*x^2 + (x^2 - 6*x^3 - 6*x^4)*Log[x])*Log[Log[x]] + (3*x - 4*x^2 - 6*x^3)*Log[x]*Log[Log[x]]^2 + (1 - 2*x^
2)*Log[x]*Log[Log[x]]^3))/(x^4*Log[x]^2 + 3*x^3*Log[x]^2*Log[Log[x]] + 3*x^2*Log[x]^2*Log[Log[x]]^2 + x*Log[x]
^2*Log[Log[x]]^3 + E^((x^2 + 2*x^3 + x^4 + (2*x^2 + 2*x^3)*Log[Log[x]] + x^2*Log[Log[x]]^2)/(x^2 + 2*x*Log[Log
[x]] + Log[Log[x]]^2))*(x^4*Log[x] + 3*x^3*Log[x]*Log[Log[x]] + 3*x^2*Log[x]*Log[Log[x]]^2 + x*Log[x]*Log[Log[
x]]^3)),x]

[Out]

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

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fricas [B]  time = 0.82, size = 61, normalized size = 2.65 \begin {gather*} \log \relax (x) - \log \left (e^{\left (\frac {x^{4} + x^{2} \log \left (\log \relax (x)\right )^{2} + 2 \, x^{3} + x^{2} + 2 \, {\left (x^{3} + x^{2}\right )} \log \left (\log \relax (x)\right )}{x^{2} + 2 \, x \log \left (\log \relax (x)\right ) + \log \left (\log \relax (x)\right )^{2}}\right )} + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+1)*log(x)*log(log(x))^3+(-6*x^3-4*x^2+3*x)*log(x)*log(log(x))^2+((-6*x^4-6*x^3+x^2)*log(x)
+2*x^2)*log(log(x))+(-2*x^5-2*x^4+x^3)*log(x)+2*x^3+2*x^2)*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^
4+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+(log(x)^2-log(x))*log(log(x))^3+(3*x*log(x)^2-3*x*log(x))*lo
g(log(x))^2+(3*x^2*log(x)^2-3*x^2*log(x))*log(log(x))+x^3*log(x)^2-x^3*log(x))/((x*log(x)*log(log(x))^3+3*x^2*
log(x)*log(log(x))^2+3*x^3*log(x)*log(log(x))+x^4*log(x))*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^4
+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+x*log(x)^2*log(log(x))^3+3*x^2*log(x)^2*log(log(x))^2+3*x^3*l
og(x)^2*log(log(x))+x^4*log(x)^2),x, algorithm="fricas")

[Out]

log(x) - log(e^((x^4 + x^2*log(log(x))^2 + 2*x^3 + x^2 + 2*(x^3 + x^2)*log(log(x)))/(x^2 + 2*x*log(log(x)) + l
og(log(x))^2)) + log(x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+1)*log(x)*log(log(x))^3+(-6*x^3-4*x^2+3*x)*log(x)*log(log(x))^2+((-6*x^4-6*x^3+x^2)*log(x)
+2*x^2)*log(log(x))+(-2*x^5-2*x^4+x^3)*log(x)+2*x^3+2*x^2)*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^
4+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+(log(x)^2-log(x))*log(log(x))^3+(3*x*log(x)^2-3*x*log(x))*lo
g(log(x))^2+(3*x^2*log(x)^2-3*x^2*log(x))*log(log(x))+x^3*log(x)^2-x^3*log(x))/((x*log(x)*log(log(x))^3+3*x^2*
log(x)*log(log(x))^2+3*x^3*log(x)*log(log(x))+x^4*log(x))*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^4
+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+x*log(x)^2*log(log(x))^3+3*x^2*log(x)^2*log(log(x))^2+3*x^3*l
og(x)^2*log(log(x))+x^4*log(x)^2),x, algorithm="giac")

[Out]

undef

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maple [B]  time = 0.09, size = 111, normalized size = 4.83

method	result	size
risch	\(\ln \relax (x )-x^{2}-\frac {\left (2 x +2 \ln \left (\ln \relax (x )\right )+1\right ) x^{2}}{\left (\ln \left (\ln \relax (x )\right )+x \right )^{2}}+\frac {x^{2} \ln \left (\ln \relax (x )\right )^{2}+\left (2 x^{3}+2 x^{2}\right ) \ln \left (\ln \relax (x )\right )+x^{4}+2 x^{3}+x^{2}}{\ln \left (\ln \relax (x )\right )^{2}+2 x \ln \left (\ln \relax (x )\right )+x^{2}}-\ln \left (\ln \relax (x )+{\mathrm e}^{\frac {x^{2} \left (\ln \left (\ln \relax (x )\right )+x +1\right )^{2}}{\left (\ln \left (\ln \relax (x )\right )+x \right )^{2}}}\right )\)	\(111\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^2+1)*ln(x)*ln(ln(x))^3+(-6*x^3-4*x^2+3*x)*ln(x)*ln(ln(x))^2+((-6*x^4-6*x^3+x^2)*ln(x)+2*x^2)*ln(ln
(x))+(-2*x^5-2*x^4+x^3)*ln(x)+2*x^3+2*x^2)*exp((x^2*ln(ln(x))^2+(2*x^3+2*x^2)*ln(ln(x))+x^4+2*x^3+x^2)/(ln(ln(
x))^2+2*x*ln(ln(x))+x^2))+(ln(x)^2-ln(x))*ln(ln(x))^3+(3*x*ln(x)^2-3*x*ln(x))*ln(ln(x))^2+(3*x^2*ln(x)^2-3*x^2
*ln(x))*ln(ln(x))+x^3*ln(x)^2-x^3*ln(x))/((x*ln(x)*ln(ln(x))^3+3*x^2*ln(x)*ln(ln(x))^2+3*x^3*ln(x)*ln(ln(x))+x
^4*ln(x))*exp((x^2*ln(ln(x))^2+(2*x^3+2*x^2)*ln(ln(x))+x^4+2*x^3+x^2)/(ln(ln(x))^2+2*x*ln(ln(x))+x^2))+x*ln(x)
^2*ln(ln(x))^3+3*x^2*ln(x)^2*ln(ln(x))^2+3*x^3*ln(x)^2*ln(ln(x))+x^4*ln(x)^2),x,method=_RETURNVERBOSE)

[Out]

ln(x)-x^2-(2*x+2*ln(ln(x))+1)*x^2/(ln(ln(x))+x)^2+(x^2*ln(ln(x))^2+(2*x^3+2*x^2)*ln(ln(x))+x^4+2*x^3+x^2)/(ln(
ln(x))^2+2*x*ln(ln(x))+x^2)-ln(ln(x)+exp(x^2*(ln(ln(x))+x+1)^2/(ln(ln(x))+x)^2))

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maxima [B]  time = 1.24, size = 124, normalized size = 5.39 \begin {gather*} -\frac {x^{3} + x^{2} \log \left (\log \relax (x)\right ) + 2 \, x^{2} + 2 \, x}{x + \log \left (\log \relax (x)\right )} - \log \left ({\left (\log \relax (x)^{\frac {2}{x + \log \left (\log \relax (x)\right )}} \log \relax (x)^{3} + e^{\left (x^{2} + 2 \, x + \frac {\log \left (\log \relax (x)\right )^{2}}{x^{2} + 2 \, x \log \left (\log \relax (x)\right ) + \log \left (\log \relax (x)\right )^{2}} + \frac {2 \, \log \left (\log \relax (x)\right )^{2}}{x + \log \left (\log \relax (x)\right )} + 1\right )}\right )} e^{\left (-x^{2} - 2 \, x - \frac {2 \, \log \left (\log \relax (x)\right )^{2}}{x + \log \left (\log \relax (x)\right )} - 1\right )}\right ) + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+1)*log(x)*log(log(x))^3+(-6*x^3-4*x^2+3*x)*log(x)*log(log(x))^2+((-6*x^4-6*x^3+x^2)*log(x)
+2*x^2)*log(log(x))+(-2*x^5-2*x^4+x^3)*log(x)+2*x^3+2*x^2)*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^
4+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+(log(x)^2-log(x))*log(log(x))^3+(3*x*log(x)^2-3*x*log(x))*lo
g(log(x))^2+(3*x^2*log(x)^2-3*x^2*log(x))*log(log(x))+x^3*log(x)^2-x^3*log(x))/((x*log(x)*log(log(x))^3+3*x^2*
log(x)*log(log(x))^2+3*x^3*log(x)*log(log(x))+x^4*log(x))*exp((x^2*log(log(x))^2+(2*x^3+2*x^2)*log(log(x))+x^4
+2*x^3+x^2)/(log(log(x))^2+2*x*log(log(x))+x^2))+x*log(x)^2*log(log(x))^3+3*x^2*log(x)^2*log(log(x))^2+3*x^3*l
og(x)^2*log(log(x))+x^4*log(x)^2),x, algorithm="maxima")

[Out]

-(x^3 + x^2*log(log(x)) + 2*x^2 + 2*x)/(x + log(log(x))) - log((log(x)^(2/(x + log(log(x))))*log(x)^3 + e^(x^2
+ 2*x + log(log(x))^2/(x^2 + 2*x*log(log(x)) + log(log(x))^2) + 2*log(log(x))^2/(x + log(log(x))) + 1))*e^(-x
^2 - 2*x - 2*log(log(x))^2/(x + log(log(x))) - 1)) + log(x)

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mupad [B]  time = 2.26, size = 156, normalized size = 6.78 \begin {gather*} \ln \relax (x)-\ln \left (\ln \relax (x)+{\mathrm {e}}^{\frac {x^2}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\,{\mathrm {e}}^{\frac {x^4}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\,{\mathrm {e}}^{\frac {2\,x^3}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\,{\mathrm {e}}^{\frac {2\,x^2\,\ln \left (\ln \relax (x)\right )}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\,{\mathrm {e}}^{\frac {2\,x^3\,\ln \left (\ln \relax (x)\right )}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\,{\mathrm {e}}^{\frac {x^2\,{\ln \left (\ln \relax (x)\right )}^2}{x^2+2\,x\,\ln \left (\ln \relax (x)\right )+{\ln \left (\ln \relax (x)\right )}^2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((log(log(x))*(2*x^2 + 2*x^3) + x^2 + 2*x^3 + x^4 + x^2*log(log(x))^2)/(2*x*log(log(x)) + log(log(x))
^2 + x^2))*(log(x)*(2*x^4 - x^3 + 2*x^5) + log(log(x))*(log(x)*(6*x^3 - x^2 + 6*x^4) - 2*x^2) - 2*x^2 - 2*x^3
+ log(log(x))^3*log(x)*(2*x^2 - 1) + log(log(x))^2*log(x)*(4*x^2 - 3*x + 6*x^3)) + x^3*log(x) - log(log(x))^2*
(3*x*log(x)^2 - 3*x*log(x)) - x^3*log(x)^2 + log(log(x))*(3*x^2*log(x) - 3*x^2*log(x)^2) + log(log(x))^3*(log(
x) - log(x)^2))/(exp((log(log(x))*(2*x^2 + 2*x^3) + x^2 + 2*x^3 + x^4 + x^2*log(log(x))^2)/(2*x*log(log(x)) +
log(log(x))^2 + x^2))*(x^4*log(x) + x*log(log(x))^3*log(x) + 3*x^3*log(log(x))*log(x) + 3*x^2*log(log(x))^2*lo
g(x)) + x^4*log(x)^2 + 3*x^2*log(log(x))^2*log(x)^2 + x*log(log(x))^3*log(x)^2 + 3*x^3*log(log(x))*log(x)^2),x
)

[Out]

log(x) - log(log(x) + exp(x^2/(2*x*log(log(x)) + log(log(x))^2 + x^2))*exp(x^4/(2*x*log(log(x)) + log(log(x))^
2 + x^2))*exp((2*x^3)/(2*x*log(log(x)) + log(log(x))^2 + x^2))*exp((2*x^2*log(log(x)))/(2*x*log(log(x)) + log(
log(x))^2 + x^2))*exp((2*x^3*log(log(x)))/(2*x*log(log(x)) + log(log(x))^2 + x^2))*exp((x^2*log(log(x))^2)/(2*
x*log(log(x)) + log(log(x))^2 + x^2)))

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sympy [B]  time = 2.92, size = 65, normalized size = 2.83 \begin {gather*} \log {\relax (x )} - \log {\left (e^{\frac {x^{4} + 2 x^{3} + x^{2} \log {\left (\log {\relax (x )} \right )}^{2} + x^{2} + \left (2 x^{3} + 2 x^{2}\right ) \log {\left (\log {\relax (x )} \right )}}{x^{2} + 2 x \log {\left (\log {\relax (x )} \right )} + \log {\left (\log {\relax (x )} \right )}^{2}}} + \log {\relax (x )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**2+1)*ln(x)*ln(ln(x))**3+(-6*x**3-4*x**2+3*x)*ln(x)*ln(ln(x))**2+((-6*x**4-6*x**3+x**2)*ln(x
)+2*x**2)*ln(ln(x))+(-2*x**5-2*x**4+x**3)*ln(x)+2*x**3+2*x**2)*exp((x**2*ln(ln(x))**2+(2*x**3+2*x**2)*ln(ln(x)
)+x**4+2*x**3+x**2)/(ln(ln(x))**2+2*x*ln(ln(x))+x**2))+(ln(x)**2-ln(x))*ln(ln(x))**3+(3*x*ln(x)**2-3*x*ln(x))*
ln(ln(x))**2+(3*x**2*ln(x)**2-3*x**2*ln(x))*ln(ln(x))+x**3*ln(x)**2-x**3*ln(x))/((x*ln(x)*ln(ln(x))**3+3*x**2*
ln(x)*ln(ln(x))**2+3*x**3*ln(x)*ln(ln(x))+x**4*ln(x))*exp((x**2*ln(ln(x))**2+(2*x**3+2*x**2)*ln(ln(x))+x**4+2*
x**3+x**2)/(ln(ln(x))**2+2*x*ln(ln(x))+x**2))+x*ln(x)**2*ln(ln(x))**3+3*x**2*ln(x)**2*ln(ln(x))**2+3*x**3*ln(x
)**2*ln(ln(x))+x**4*ln(x)**2),x)

[Out]

log(x) - log(exp((x**4 + 2*x**3 + x**2*log(log(x))**2 + x**2 + (2*x**3 + 2*x**2)*log(log(x)))/(x**2 + 2*x*log(
log(x)) + log(log(x))**2)) + log(x))

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