3.11.72 \(\int \frac {-2 x^2-2 x \log (x)+(-2 x-4 x^2-2 x \log (x)) \log (25 x)+(2 x^2+2 x \log (x)) \log (25 x) \log (x+\log (x))+(2 x^2+2 x \log (x)) \log (25 x) \log (\log (25 x))}{(-x-3 x^2-3 x^3-x^4+(-1-3 x-3 x^2-x^3) \log (x)) \log (25 x)+(3 x+6 x^2+3 x^3+(3+6 x+3 x^2) \log (x)) \log (25 x) \log (x+\log (x))+(-3 x-3 x^2+(-3-3 x) \log (x)) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+((3 x+6 x^2+3 x^3+(3+6 x+3 x^2) \log (x)) \log (25 x)+(-6 x-6 x^2+(-6-6 x) \log (x)) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))) \log (\log (25 x))+((-3 x-3 x^2+(-3-3 x) \log (x)) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx\) [1072]
Optimal. Leaf size=21 \[ \frac {x^2}{(-1-x+\log (x+\log (x))+\log (\log (25 x)))^2} \]
[Out]
x^2/(ln(x+ln(x))+ln(ln(25*x))-1-x)^2
________________________________________________________________________________________
Rubi [F]
time = 3.94, 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 {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-2*x^2 - 2*x*Log[x] + (-2*x - 4*x^2 - 2*x*Log[x])*Log[25*x] + (2*x^2 + 2*x*Log[x])*Log[25*x]*Log[x + Log[
x]] + (2*x^2 + 2*x*Log[x])*Log[25*x]*Log[Log[25*x]])/((-x - 3*x^2 - 3*x^3 - x^4 + (-1 - 3*x - 3*x^2 - x^3)*Log
[x])*Log[25*x] + (3*x + 6*x^2 + 3*x^3 + (3 + 6*x + 3*x^2)*Log[x])*Log[25*x]*Log[x + Log[x]] + (-3*x - 3*x^2 +
(-3 - 3*x)*Log[x])*Log[25*x]*Log[x + Log[x]]^2 + (x + Log[x])*Log[25*x]*Log[x + Log[x]]^3 + ((3*x + 6*x^2 + 3*
x^3 + (3 + 6*x + 3*x^2)*Log[x])*Log[25*x] + (-6*x - 6*x^2 + (-6 - 6*x)*Log[x])*Log[25*x]*Log[x + Log[x]] + (3*
x + 3*Log[x])*Log[25*x]*Log[x + Log[x]]^2)*Log[Log[25*x]] + ((-3*x - 3*x^2 + (-3 - 3*x)*Log[x])*Log[25*x] + (3
*x + 3*Log[x])*Log[25*x]*Log[x + Log[x]])*Log[Log[25*x]]^2 + (x + Log[x])*Log[25*x]*Log[Log[25*x]]^3),x]
[Out]
2*Defer[Int][x/((x + Log[x])*(1 + x - Log[x + Log[x]] - Log[Log[25*x]])^3), x] + 2*Defer[Int][x^2/((x + Log[x]
)*(1 + x - Log[x + Log[x]] - Log[Log[25*x]])^3), x] - 2*Defer[Int][x^3/((x + Log[x])*(1 + x - Log[x + Log[x]]
- Log[Log[25*x]])^3), x] - 2*Defer[Int][(x^2*Log[x])/((x + Log[x])*(1 + x - Log[x + Log[x]] - Log[Log[25*x]])^
3), x] + 2*Defer[Int][x^2/((x + Log[x])*Log[25*x]*(1 + x - Log[x + Log[x]] - Log[Log[25*x]])^3), x] + 2*Defer[
Int][(x*Log[x])/((x + Log[x])*Log[25*x]*(1 + x - Log[x + Log[x]] - Log[Log[25*x]])^3), x] + 2*Defer[Int][x/(1
+ x - Log[x + Log[x]] - Log[Log[25*x]])^2, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x (x-\log (25 x) (-1-2 x+x \log (x+\log (x))+x \log (\log (25 x)))-\log (x) (-1+\log (25 x) (-1+\log (x+\log (x))+\log (\log (25 x)))))}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx\\ &=2 \int \frac {x (x-\log (25 x) (-1-2 x+x \log (x+\log (x))+x \log (\log (25 x)))-\log (x) (-1+\log (25 x) (-1+\log (x+\log (x))+\log (\log (25 x)))))}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx\\ &=2 \int \left (-\frac {x \left (-x-\log (x)-\log (25 x)-x \log (25 x)+x^2 \log (25 x)+x \log (x) \log (25 x)\right )}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2}\right ) \, dx\\ &=-\left (2 \int \frac {x \left (-x-\log (x)-\log (25 x)-x \log (25 x)+x^2 \log (25 x)+x \log (x) \log (25 x)\right )}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx\right )+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx\\ &=-\left (2 \int \left (-\frac {x}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x^2}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x^3}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x^2 \log (x)}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x^2}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x \log (x)}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}\right ) \, dx\right )+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx\\ &=2 \int \frac {x}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x^2}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx-2 \int \frac {x^3}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx-2 \int \frac {x^2 \log (x)}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x^2}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x \log (x)}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 21, normalized size = 1.00 \begin {gather*} \frac {x^2}{(-1-x+\log (x+\log (x))+\log (\log (25 x)))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-2*x^2 - 2*x*Log[x] + (-2*x - 4*x^2 - 2*x*Log[x])*Log[25*x] + (2*x^2 + 2*x*Log[x])*Log[25*x]*Log[x
+ Log[x]] + (2*x^2 + 2*x*Log[x])*Log[25*x]*Log[Log[25*x]])/((-x - 3*x^2 - 3*x^3 - x^4 + (-1 - 3*x - 3*x^2 - x^
3)*Log[x])*Log[25*x] + (3*x + 6*x^2 + 3*x^3 + (3 + 6*x + 3*x^2)*Log[x])*Log[25*x]*Log[x + Log[x]] + (-3*x - 3*
x^2 + (-3 - 3*x)*Log[x])*Log[25*x]*Log[x + Log[x]]^2 + (x + Log[x])*Log[25*x]*Log[x + Log[x]]^3 + ((3*x + 6*x^
2 + 3*x^3 + (3 + 6*x + 3*x^2)*Log[x])*Log[25*x] + (-6*x - 6*x^2 + (-6 - 6*x)*Log[x])*Log[25*x]*Log[x + Log[x]]
+ (3*x + 3*Log[x])*Log[25*x]*Log[x + Log[x]]^2)*Log[Log[25*x]] + ((-3*x - 3*x^2 + (-3 - 3*x)*Log[x])*Log[25*x
] + (3*x + 3*Log[x])*Log[25*x]*Log[x + Log[x]])*Log[Log[25*x]]^2 + (x + Log[x])*Log[25*x]*Log[Log[25*x]]^3),x]
[Out]
x^2/(-1 - x + Log[x + Log[x]] + Log[Log[25*x]])^2
________________________________________________________________________________________
Maple [A]
time = 42.30, size = 27, normalized size = 1.29
| | |
| method |
result |
size |
| | |
| default |
\(\frac {x^{2}}{\left (x -\ln \left (2 \ln \left (5\right )+\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )+1\right )^{2}}\) |
\(27\) |
| risch |
\(\frac {x^{2}}{\left (x -\ln \left (2 \ln \left (5\right )+\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )+1\right )^{2}}\) |
\(27\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((2*x*ln(x)+2*x^2)*ln(25*x)*ln(ln(25*x))+(2*x*ln(x)+2*x^2)*ln(25*x)*ln(x+ln(x))+(-2*x*ln(x)-4*x^2-2*x)*ln(
25*x)-2*x*ln(x)-2*x^2)/((x+ln(x))*ln(25*x)*ln(ln(25*x))^3+((3*x+3*ln(x))*ln(25*x)*ln(x+ln(x))+((-3*x-3)*ln(x)-
3*x^2-3*x)*ln(25*x))*ln(ln(25*x))^2+((3*x+3*ln(x))*ln(25*x)*ln(x+ln(x))^2+((-6*x-6)*ln(x)-6*x^2-6*x)*ln(25*x)*
ln(x+ln(x))+((3*x^2+6*x+3)*ln(x)+3*x^3+6*x^2+3*x)*ln(25*x))*ln(ln(25*x))+(x+ln(x))*ln(25*x)*ln(x+ln(x))^3+((-3
*x-3)*ln(x)-3*x^2-3*x)*ln(25*x)*ln(x+ln(x))^2+((3*x^2+6*x+3)*ln(x)+3*x^3+6*x^2+3*x)*ln(25*x)*ln(x+ln(x))+((-x^
3-3*x^2-3*x-1)*ln(x)-x^4-3*x^3-3*x^2-x)*ln(25*x)),x,method=_RETURNVERBOSE)
[Out]
x^2/(x-ln(2*ln(5)+ln(x))-ln(x+ln(x))+1)^2
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 61 vs.
\(2 (23) = 46\).
time = 0.74, size = 61, normalized size = 2.90 \begin {gather*} \frac {x^{2}}{x^{2} - 2 \, {\left (x + 1\right )} \log \left (x + \log \left (x\right )\right ) + \log \left (x + \log \left (x\right )\right )^{2} - 2 \, {\left (x - \log \left (x + \log \left (x\right )\right ) + 1\right )} \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right ) + \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right )^{2} + 2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x*log(x)+2*x^2)*log(25*x)*log(log(25*x))+(2*x*log(x)+2*x^2)*log(25*x)*log(x+log(x))+(-2*x*log(x)
-4*x^2-2*x)*log(25*x)-2*x*log(x)-2*x^2)/((x+log(x))*log(25*x)*log(log(25*x))^3+((3*x+3*log(x))*log(25*x)*log(x
+log(x))+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x))*log(log(25*x))^2+((3*x+3*log(x))*log(25*x)*log(x+log(x))^2+((-
6*x-6)*log(x)-6*x^2-6*x)*log(25*x)*log(x+log(x))+((3*x^2+6*x+3)*log(x)+3*x^3+6*x^2+3*x)*log(25*x))*log(log(25*
x))+(x+log(x))*log(25*x)*log(x+log(x))^3+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x)*log(x+log(x))^2+((3*x^2+6*x+3)*
log(x)+3*x^3+6*x^2+3*x)*log(25*x)*log(x+log(x))+((-x^3-3*x^2-3*x-1)*log(x)-x^4-3*x^3-3*x^2-x)*log(25*x)),x, al
gorithm="maxima")
[Out]
x^2/(x^2 - 2*(x + 1)*log(x + log(x)) + log(x + log(x))^2 - 2*(x - log(x + log(x)) + 1)*log(2*log(5) + log(x))
+ log(2*log(5) + log(x))^2 + 2*x + 1)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 61 vs.
\(2 (23) = 46\).
time = 0.38, size = 61, normalized size = 2.90 \begin {gather*} \frac {x^{2}}{x^{2} - 2 \, {\left (x + 1\right )} \log \left (x + \log \left (x\right )\right ) + \log \left (x + \log \left (x\right )\right )^{2} - 2 \, {\left (x - \log \left (x + \log \left (x\right )\right ) + 1\right )} \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right ) + \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right )^{2} + 2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x*log(x)+2*x^2)*log(25*x)*log(log(25*x))+(2*x*log(x)+2*x^2)*log(25*x)*log(x+log(x))+(-2*x*log(x)
-4*x^2-2*x)*log(25*x)-2*x*log(x)-2*x^2)/((x+log(x))*log(25*x)*log(log(25*x))^3+((3*x+3*log(x))*log(25*x)*log(x
+log(x))+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x))*log(log(25*x))^2+((3*x+3*log(x))*log(25*x)*log(x+log(x))^2+((-
6*x-6)*log(x)-6*x^2-6*x)*log(25*x)*log(x+log(x))+((3*x^2+6*x+3)*log(x)+3*x^3+6*x^2+3*x)*log(25*x))*log(log(25*
x))+(x+log(x))*log(25*x)*log(x+log(x))^3+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x)*log(x+log(x))^2+((3*x^2+6*x+3)*
log(x)+3*x^3+6*x^2+3*x)*log(25*x)*log(x+log(x))+((-x^3-3*x^2-3*x-1)*log(x)-x^4-3*x^3-3*x^2-x)*log(25*x)),x, al
gorithm="fricas")
[Out]
x^2/(x^2 - 2*(x + 1)*log(x + log(x)) + log(x + log(x))^2 - 2*(x - log(x + log(x)) + 1)*log(2*log(5) + log(x))
+ log(2*log(5) + log(x))^2 + 2*x + 1)
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 70 vs.
\(2 (20) = 40\).
time = 0.60, size = 70, normalized size = 3.33 \begin {gather*} \frac {x^{2}}{x^{2} - 2 x \log {\left (x + \log {\left (x \right )} \right )} + 2 x + \left (- 2 x + 2 \log {\left (x + \log {\left (x \right )} \right )} - 2\right ) \log {\left (\log {\left (x \right )} + \log {\left (25 \right )} \right )} + \log {\left (x + \log {\left (x \right )} \right )}^{2} - 2 \log {\left (x + \log {\left (x \right )} \right )} + \log {\left (\log {\left (x \right )} + \log {\left (25 \right )} \right )}^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x*ln(x)+2*x**2)*ln(25*x)*ln(ln(25*x))+(2*x*ln(x)+2*x**2)*ln(25*x)*ln(x+ln(x))+(-2*x*ln(x)-4*x**2
-2*x)*ln(25*x)-2*x*ln(x)-2*x**2)/((x+ln(x))*ln(25*x)*ln(ln(25*x))**3+((3*x+3*ln(x))*ln(25*x)*ln(x+ln(x))+((-3*
x-3)*ln(x)-3*x**2-3*x)*ln(25*x))*ln(ln(25*x))**2+((3*x+3*ln(x))*ln(25*x)*ln(x+ln(x))**2+((-6*x-6)*ln(x)-6*x**2
-6*x)*ln(25*x)*ln(x+ln(x))+((3*x**2+6*x+3)*ln(x)+3*x**3+6*x**2+3*x)*ln(25*x))*ln(ln(25*x))+(x+ln(x))*ln(25*x)*
ln(x+ln(x))**3+((-3*x-3)*ln(x)-3*x**2-3*x)*ln(25*x)*ln(x+ln(x))**2+((3*x**2+6*x+3)*ln(x)+3*x**3+6*x**2+3*x)*ln
(25*x)*ln(x+ln(x))+((-x**3-3*x**2-3*x-1)*ln(x)-x**4-3*x**3-3*x**2-x)*ln(25*x)),x)
[Out]
x**2/(x**2 - 2*x*log(x + log(x)) + 2*x + (-2*x + 2*log(x + log(x)) - 2)*log(log(x) + log(25)) + log(x + log(x)
)**2 - 2*log(x + log(x)) + log(log(x) + log(25))**2 + 1)
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 900 vs.
\(2 (23) = 46\).
time = 0.76, size = 900, normalized size = 42.86 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((2*x*log(x)+2*x^2)*log(25*x)*log(log(25*x))+(2*x*log(x)+2*x^2)*log(25*x)*log(x+log(x))+(-2*x*log(x)
-4*x^2-2*x)*log(25*x)-2*x*log(x)-2*x^2)/((x+log(x))*log(25*x)*log(log(25*x))^3+((3*x+3*log(x))*log(25*x)*log(x
+log(x))+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x))*log(log(25*x))^2+((3*x+3*log(x))*log(25*x)*log(x+log(x))^2+((-
6*x-6)*log(x)-6*x^2-6*x)*log(25*x)*log(x+log(x))+((3*x^2+6*x+3)*log(x)+3*x^3+6*x^2+3*x)*log(25*x))*log(log(25*
x))+(x+log(x))*log(25*x)*log(x+log(x))^3+((-3*x-3)*log(x)-3*x^2-3*x)*log(25*x)*log(x+log(x))^2+((3*x^2+6*x+3)*
log(x)+3*x^3+6*x^2+3*x)*log(25*x)*log(x+log(x))+((-x^3-3*x^2-3*x-1)*log(x)-x^4-3*x^3-3*x^2-x)*log(25*x)),x, al
gorithm="giac")
[Out]
(2*x^4*log(5) + x^4*log(x) + 2*x^3*log(5)*log(x) + x^3*log(x)^2 - 2*x^3*log(5) - x^3*log(x) - x^3 - 2*x^2*log(
5) - 2*x^2*log(x))/(2*x^4*log(5) - 4*x^3*log(5)*log(x + log(x)) + 2*x^2*log(5)*log(x + log(x))^2 + x^4*log(x)
+ 2*x^3*log(5)*log(x) - 2*x^3*log(x + log(x))*log(x) - 4*x^2*log(5)*log(x + log(x))*log(x) + x^2*log(x + log(x
))^2*log(x) + 2*x*log(5)*log(x + log(x))^2*log(x) + x^3*log(x)^2 - 2*x^2*log(x + log(x))*log(x)^2 + x*log(x +
log(x))^2*log(x)^2 - 4*x^3*log(5)*log(2*log(5) + log(x)) + 4*x^2*log(5)*log(x + log(x))*log(2*log(5) + log(x))
- 2*x^3*log(x)*log(2*log(5) + log(x)) - 4*x^2*log(5)*log(x)*log(2*log(5) + log(x)) + 2*x^2*log(x + log(x))*lo
g(x)*log(2*log(5) + log(x)) + 4*x*log(5)*log(x + log(x))*log(x)*log(2*log(5) + log(x)) - 2*x^2*log(x)^2*log(2*
log(5) + log(x)) + 2*x*log(x + log(x))*log(x)^2*log(2*log(5) + log(x)) + 2*x^2*log(5)*log(2*log(5) + log(x))^2
+ x^2*log(x)*log(2*log(5) + log(x))^2 + 2*x*log(5)*log(x)*log(2*log(5) + log(x))^2 + x*log(x)^2*log(2*log(5)
+ log(x))^2 + 2*x^3*log(5) - 2*x*log(5)*log(x + log(x))^2 + x^3*log(x) + 4*x^2*log(5)*log(x) - 4*x*log(5)*log(
x + log(x))*log(x) - x*log(x + log(x))^2*log(x) + 2*x^2*log(x)^2 - 2*x*log(x + log(x))*log(x)^2 - 4*x*log(5)*l
og(x + log(x))*log(2*log(5) + log(x)) - 4*x*log(5)*log(x)*log(2*log(5) + log(x)) - 2*x*log(x + log(x))*log(x)*
log(2*log(5) + log(x)) - 2*x*log(x)^2*log(2*log(5) + log(x)) - 2*x*log(5)*log(2*log(5) + log(x))^2 - x*log(x)*
log(2*log(5) + log(x))^2 - x^3 - 4*x^2*log(5) + 2*x^2*log(x + log(x)) + 8*x*log(5)*log(x + log(x)) - x*log(x +
log(x))^2 - 2*log(5)*log(x + log(x))^2 - 3*x^2*log(x) + 2*x*log(5)*log(x) + 6*x*log(x + log(x))*log(x) - 2*lo
g(x + log(x))^2*log(x) + x*log(x)^2 + 2*x^2*log(2*log(5) + log(x)) + 8*x*log(5)*log(2*log(5) + log(x)) - 2*x*l
og(x + log(x))*log(2*log(5) + log(x)) - 4*log(5)*log(x + log(x))*log(2*log(5) + log(x)) + 6*x*log(x)*log(2*log
(5) + log(x)) - 4*log(x + log(x))*log(x)*log(2*log(5) + log(x)) - x*log(2*log(5) + log(x))^2 - 2*log(5)*log(2*
log(5) + log(x))^2 - 2*log(x)*log(2*log(5) + log(x))^2 - 2*x^2 - 6*x*log(5) + 2*x*log(x + log(x)) + 4*log(5)*l
og(x + log(x)) - 5*x*log(x) + 4*log(x + log(x))*log(x) + 2*x*log(2*log(5) + log(x)) + 4*log(5)*log(2*log(5) +
log(x)) + 4*log(x)*log(2*log(5) + log(x)) - x - 2*log(5) - 2*log(x))
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int -\frac {2\,x\,\ln \left (x\right )+\ln \left (25\,x\right )\,\left (2\,x+2\,x\,\ln \left (x\right )+4\,x^2\right )+2\,x^2-\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (2\,x\,\ln \left (x\right )+2\,x^2\right )-\ln \left (25\,x\right )\,\ln \left (\ln \left (25\,x\right )\right )\,\left (2\,x\,\ln \left (x\right )+2\,x^2\right )}{\ln \left (\ln \left (25\,x\right )\right )\,\left (\ln \left (25\,x\right )\,\left (3\,x+3\,\ln \left (x\right )\right )\,{\ln \left (x+\ln \left (x\right )\right )}^2-\ln \left (25\,x\right )\,\left (6\,x+\ln \left (x\right )\,\left (6\,x+6\right )+6\,x^2\right )\,\ln \left (x+\ln \left (x\right )\right )+\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x^2+6\,x+3\right )+6\,x^2+3\,x^3\right )\right )-{\ln \left (\ln \left (25\,x\right )\right )}^2\,\left (\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x+3\right )+3\,x^2\right )-\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (3\,x+3\,\ln \left (x\right )\right )\right )-\ln \left (25\,x\right )\,\left (x+\ln \left (x\right )\,\left (x^3+3\,x^2+3\,x+1\right )+3\,x^2+3\,x^3+x^4\right )-{\ln \left (x+\ln \left (x\right )\right )}^2\,\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x+3\right )+3\,x^2\right )+\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x^2+6\,x+3\right )+6\,x^2+3\,x^3\right )+\ln \left (25\,x\right )\,{\ln \left (\ln \left (25\,x\right )\right )}^3\,\left (x+\ln \left (x\right )\right )+{\ln \left (x+\ln \left (x\right )\right )}^3\,\ln \left (25\,x\right )\,\left (x+\ln \left (x\right )\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(2*x*log(x) + log(25*x)*(2*x + 2*x*log(x) + 4*x^2) + 2*x^2 - log(x + log(x))*log(25*x)*(2*x*log(x) + 2*x^
2) - log(25*x)*log(log(25*x))*(2*x*log(x) + 2*x^2))/(log(log(25*x))*(log(25*x)*(3*x + log(x)*(6*x + 3*x^2 + 3)
+ 6*x^2 + 3*x^3) + log(x + log(x))^2*log(25*x)*(3*x + 3*log(x)) - log(x + log(x))*log(25*x)*(6*x + log(x)*(6*
x + 6) + 6*x^2)) - log(log(25*x))^2*(log(25*x)*(3*x + log(x)*(3*x + 3) + 3*x^2) - log(x + log(x))*log(25*x)*(3
*x + 3*log(x))) - log(25*x)*(x + log(x)*(3*x + 3*x^2 + x^3 + 1) + 3*x^2 + 3*x^3 + x^4) - log(x + log(x))^2*log
(25*x)*(3*x + log(x)*(3*x + 3) + 3*x^2) + log(x + log(x))*log(25*x)*(3*x + log(x)*(6*x + 3*x^2 + 3) + 6*x^2 +
3*x^3) + log(25*x)*log(log(25*x))^3*(x + log(x)) + log(x + log(x))^3*log(25*x)*(x + log(x))),x)
[Out]
int(-(2*x*log(x) + log(25*x)*(2*x + 2*x*log(x) + 4*x^2) + 2*x^2 - log(x + log(x))*log(25*x)*(2*x*log(x) + 2*x^
2) - log(25*x)*log(log(25*x))*(2*x*log(x) + 2*x^2))/(log(log(25*x))*(log(25*x)*(3*x + log(x)*(6*x + 3*x^2 + 3)
+ 6*x^2 + 3*x^3) + log(x + log(x))^2*log(25*x)*(3*x + 3*log(x)) - log(x + log(x))*log(25*x)*(6*x + log(x)*(6*
x + 6) + 6*x^2)) - log(log(25*x))^2*(log(25*x)*(3*x + log(x)*(3*x + 3) + 3*x^2) - log(x + log(x))*log(25*x)*(3
*x + 3*log(x))) - log(25*x)*(x + log(x)*(3*x + 3*x^2 + x^3 + 1) + 3*x^2 + 3*x^3 + x^4) - log(x + log(x))^2*log
(25*x)*(3*x + log(x)*(3*x + 3) + 3*x^2) + log(x + log(x))*log(25*x)*(3*x + log(x)*(6*x + 3*x^2 + 3) + 6*x^2 +
3*x^3) + log(25*x)*log(log(25*x))^3*(x + log(x)) + log(x + log(x))^3*log(25*x)*(x + log(x))), x)
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