3.99.70 \(\int \frac {(-75-53 x-2 x^2) \log ^2(25+x)+(-15 x-5 x^2) \log (\frac {1}{3} (-3 x-x^2))+(-1125-420 x-15 x^2) \log (25+x) \log (\frac {1}{3} (-3 x-x^2))+(225+84 x+3 x^2) \log ^2(25+x) \log (\frac {1}{3} (-3 x-x^2)) \log (\log (\frac {1}{3} (-3 x-x^2)))+((375+140 x+5 x^2) \log (25+x) \log (\frac {1}{3} (-3 x-x^2))+(-75-28 x-x^2) \log ^2(25+x) \log (\frac {1}{3} (-3 x-x^2)) \log (\log (\frac {1}{3} (-3 x-x^2)))) \log (\frac {5-\log (25+x) \log (\log (\frac {1}{3} (-3 x-x^2)))}{\log (25+x)})}{(-375-140 x-5 x^2) \log (25+x) \log (\frac {1}{3} (-3 x-x^2))+(75+28 x+x^2) \log ^2(25+x) \log (\frac {1}{3} (-3 x-x^2)) \log (\log (\frac {1}{3} (-3 x-x^2)))} \, dx\)

Optimal. Leaf size=30 \[ x \left (3-\log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (\frac {1}{3} (-3-x) x\right )\right )\right )\right ) \]

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Rubi [F]  time = 4.83, 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 {\left (-75-53 x-2 x^2\right ) \log ^2(25+x)+\left (-15 x-5 x^2\right ) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )+\left (-1125-420 x-15 x^2\right ) \log (25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )+\left (225+84 x+3 x^2\right ) \log ^2(25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )\right )+\left (\left (375+140 x+5 x^2\right ) \log (25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )+\left (-75-28 x-x^2\right ) \log ^2(25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )\right )\right ) \log \left (\frac {5-\log (25+x) \log \left (\log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )\right )}{\log (25+x)}\right )}{\left (-375-140 x-5 x^2\right ) \log (25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )+\left (75+28 x+x^2\right ) \log ^2(25+x) \log \left (\frac {1}{3} \left (-3 x-x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (-3 x-x^2\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-75 - 53*x - 2*x^2)*Log[25 + x]^2 + (-15*x - 5*x^2)*Log[(-3*x - x^2)/3] + (-1125 - 420*x - 15*x^2)*Log[2
5 + x]*Log[(-3*x - x^2)/3] + (225 + 84*x + 3*x^2)*Log[25 + x]^2*Log[(-3*x - x^2)/3]*Log[Log[(-3*x - x^2)/3]] +
((375 + 140*x + 5*x^2)*Log[25 + x]*Log[(-3*x - x^2)/3] + (-75 - 28*x - x^2)*Log[25 + x]^2*Log[(-3*x - x^2)/3]
*Log[Log[(-3*x - x^2)/3]])*Log[(5 - Log[25 + x]*Log[Log[(-3*x - x^2)/3]])/Log[25 + x]])/((-375 - 140*x - 5*x^2
)*Log[25 + x]*Log[(-3*x - x^2)/3] + (75 + 28*x + x^2)*Log[25 + x]^2*Log[(-3*x - x^2)/3]*Log[Log[(-3*x - x^2)/3
]]),x]

[Out]

3*x - 5*Defer[Int][1/(Log[25 + x]*(-5 + Log[25 + x]*Log[Log[-1/3*(x*(3 + x))]])), x] + 125*Defer[Int][1/((25 +
x)*Log[25 + x]*(-5 + Log[25 + x]*Log[Log[-1/3*(x*(3 + x))]])), x] - 2*Defer[Int][Log[25 + x]/(Log[-1/3*(x*(3
+ x))]*(-5 + Log[25 + x]*Log[Log[-1/3*(x*(3 + x))]])), x] + 3*Defer[Int][Log[25 + x]/((3 + x)*Log[-1/3*(x*(3 +
x))]*(-5 + Log[25 + x]*Log[Log[-1/3*(x*(3 + x))]])), x] - Defer[Int][Log[5/Log[25 + x] - Log[Log[-1/3*(x*(3 +
x))]]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {15}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )}-\frac {5 x}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}+\frac {\log (25+x) \left (-3-2 x+3 (3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}-\log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )\right ) \, dx\\ &=-\left (5 \int \frac {x}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx\right )-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+\int \frac {\log (25+x) \left (-3-2 x+3 (3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=-\left (5 \int \left (\frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}-\frac {25}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}\right ) \, dx\right )-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+\int \left (3+\frac {45 \log \left (-\frac {1}{3} x (3+x)\right )+15 x \log \left (-\frac {1}{3} x (3+x)\right )-3 \log (25+x)-2 x \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}\right ) \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=3 x-5 \int \frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+125 \int \frac {1}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+\int \frac {45 \log \left (-\frac {1}{3} x (3+x)\right )+15 x \log \left (-\frac {1}{3} x (3+x)\right )-3 \log (25+x)-2 x \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=3 x-5 \int \frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+125 \int \frac {1}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+\int \left (\frac {45}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}+\frac {15 x}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}-\frac {3 \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}-\frac {2 x \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}\right ) \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=3 x-2 \int \frac {x \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-3 \int \frac {\log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-5 \int \frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+15 \int \frac {x}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+45 \int \frac {1}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+125 \int \frac {1}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=3 x-2 \int \left (\frac {\log (25+x)}{\log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}-\frac {3 \log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}\right ) \, dx-3 \int \frac {\log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-5 \int \frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-15 \int \frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )} \, dx+15 \int \left (\frac {1}{-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )}-\frac {3}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )}\right ) \, dx+45 \int \frac {1}{(3+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+125 \int \frac {1}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ &=3 x-2 \int \frac {\log (25+x)}{\log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-3 \int \frac {\log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-5 \int \frac {1}{\log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+6 \int \frac {\log (25+x)}{(3+x) \log \left (-\frac {1}{3} x (3+x)\right ) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx+125 \int \frac {1}{(25+x) \log (25+x) \left (-5+\log (25+x) \log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right )} \, dx-\int \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.45, size = 29, normalized size = 0.97 \begin {gather*} 3 x-x \log \left (\frac {5}{\log (25+x)}-\log \left (\log \left (-\frac {1}{3} x (3+x)\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-75 - 53*x - 2*x^2)*Log[25 + x]^2 + (-15*x - 5*x^2)*Log[(-3*x - x^2)/3] + (-1125 - 420*x - 15*x^2)
*Log[25 + x]*Log[(-3*x - x^2)/3] + (225 + 84*x + 3*x^2)*Log[25 + x]^2*Log[(-3*x - x^2)/3]*Log[Log[(-3*x - x^2)
/3]] + ((375 + 140*x + 5*x^2)*Log[25 + x]*Log[(-3*x - x^2)/3] + (-75 - 28*x - x^2)*Log[25 + x]^2*Log[(-3*x - x
^2)/3]*Log[Log[(-3*x - x^2)/3]])*Log[(5 - Log[25 + x]*Log[Log[(-3*x - x^2)/3]])/Log[25 + x]])/((-375 - 140*x -
5*x^2)*Log[25 + x]*Log[(-3*x - x^2)/3] + (75 + 28*x + x^2)*Log[25 + x]^2*Log[(-3*x - x^2)/3]*Log[Log[(-3*x -
x^2)/3]]),x]

[Out]

3*x - x*Log[5/Log[25 + x] - Log[Log[-1/3*(x*(3 + x))]]]

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fricas [A]  time = 0.74, size = 34, normalized size = 1.13 \begin {gather*} -x \log \left (-\frac {\log \left (x + 25\right ) \log \left (\log \left (-\frac {1}{3} \, x^{2} - x\right )\right ) - 5}{\log \left (x + 25\right )}\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-28*x-75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(5*x^2+140*x+375)*log(-1/3*x^2-x)*
log(x+25))*log((-log(x+25)*log(log(-1/3*x^2-x))+5)/log(x+25))+(3*x^2+84*x+225)*log(-1/3*x^2-x)*log(x+25)^2*log
(log(-1/3*x^2-x))+(-2*x^2-53*x-75)*log(x+25)^2+(-15*x^2-420*x-1125)*log(-1/3*x^2-x)*log(x+25)+(-5*x^2-15*x)*lo
g(-1/3*x^2-x))/((x^2+28*x+75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(-5*x^2-140*x-375)*log(-1/3*x^2
-x)*log(x+25)),x, algorithm="fricas")

[Out]

-x*log(-(log(x + 25)*log(log(-1/3*x^2 - x)) - 5)/log(x + 25)) + 3*x

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giac [A]  time = 1.53, size = 34, normalized size = 1.13 \begin {gather*} -x \log \left (-\log \left (x + 25\right ) \log \left (\log \left (-\frac {1}{3} \, x^{2} - x\right )\right ) + 5\right ) + x \log \left (\log \left (x + 25\right )\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-28*x-75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(5*x^2+140*x+375)*log(-1/3*x^2-x)*
log(x+25))*log((-log(x+25)*log(log(-1/3*x^2-x))+5)/log(x+25))+(3*x^2+84*x+225)*log(-1/3*x^2-x)*log(x+25)^2*log
(log(-1/3*x^2-x))+(-2*x^2-53*x-75)*log(x+25)^2+(-15*x^2-420*x-1125)*log(-1/3*x^2-x)*log(x+25)+(-5*x^2-15*x)*lo
g(-1/3*x^2-x))/((x^2+28*x+75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(-5*x^2-140*x-375)*log(-1/3*x^2
-x)*log(x+25)),x, algorithm="giac")

[Out]

-x*log(-log(x + 25)*log(log(-1/3*x^2 - x)) + 5) + x*log(log(x + 25)) + 3*x

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maple [C]  time = 2.70, size = 876, normalized size = 29.20

method	result	size
risch	\(-x \ln \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )+x \ln \left (\ln \left (x +25\right )\right )+i \pi x \mathrm {csgn}\left (\frac {i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )}{\ln \left (x +25\right )}\right )^{2}+\frac {i \pi x \,\mathrm {csgn}\left (i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )\right ) \mathrm {csgn}\left (\frac {i}{\ln \left (x +25\right )}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )}{\ln \left (x +25\right )}\right )}{2}-\frac {i \pi x \,\mathrm {csgn}\left (i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )}{\ln \left (x +25\right )}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {csgn}\left (\frac {i}{\ln \left (x +25\right )}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )}{\ln \left (x +25\right )}\right )^{2}}{2}-\frac {i \pi x \mathrm {csgn}\left (\frac {i \left (\ln \left (x +25\right ) \ln \left (-\ln \relax (3)+i \pi +\ln \relax (x )+\ln \left (3+x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (3+x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (3+x \right )\right )+\mathrm {csgn}\left (i \left (3+x \right )\right )\right )}{2}+i \pi \mathrm {csgn}\left (i x \left (3+x \right )\right )^{2} \left (\mathrm {csgn}\left (i x \left (3+x \right )\right )-1\right )\right )-5\right )}{\ln \left (x +25\right )}\right )^{3}}{2}-i \pi x +3 x\)	\(876\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^2-28*x-75)*ln(-1/3*x^2-x)*ln(x+25)^2*ln(ln(-1/3*x^2-x))+(5*x^2+140*x+375)*ln(-1/3*x^2-x)*ln(x+25))*l
n((-ln(x+25)*ln(ln(-1/3*x^2-x))+5)/ln(x+25))+(3*x^2+84*x+225)*ln(-1/3*x^2-x)*ln(x+25)^2*ln(ln(-1/3*x^2-x))+(-2
*x^2-53*x-75)*ln(x+25)^2+(-15*x^2-420*x-1125)*ln(-1/3*x^2-x)*ln(x+25)+(-5*x^2-15*x)*ln(-1/3*x^2-x))/((x^2+28*x
+75)*ln(-1/3*x^2-x)*ln(x+25)^2*ln(ln(-1/3*x^2-x))+(-5*x^2-140*x-375)*ln(-1/3*x^2-x)*ln(x+25)),x,method=_RETURN
VERBOSE)

[Out]

-x*ln(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(
3+x))+csgn(I*(3+x)))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5)+x*ln(ln(x+25))+I*Pi*x*csgn(I*(ln(x+25)*ln(
-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))+csgn(I*(3+x)
))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5)/ln(x+25))^2+1/2*I*Pi*x*csgn(I*(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)
+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))+csgn(I*(3+x)))+I*Pi*csgn(I*x*
(3+x))^2*(csgn(I*x*(3+x))-1))-5))*csgn(I/ln(x+25))*csgn(I*(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn
(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))+csgn(I*(3+x)))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+
x))-1))-5)/ln(x+25))-1/2*I*Pi*x*csgn(I*(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(
I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))+csgn(I*(3+x)))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5))*csgn(I*
(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))
+csgn(I*(3+x)))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5)/ln(x+25))^2-1/2*I*Pi*x*csgn(I/ln(x+25))*csgn(I*
(ln(x+25)*ln(-ln(3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))
+csgn(I*(3+x)))+I*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5)/ln(x+25))^2-1/2*I*Pi*x*csgn(I*(ln(x+25)*ln(-ln(
3)+I*Pi+ln(x)+ln(3+x)-1/2*I*Pi*csgn(I*x*(3+x))*(-csgn(I*x*(3+x))+csgn(I*x))*(-csgn(I*x*(3+x))+csgn(I*(3+x)))+I
*Pi*csgn(I*x*(3+x))^2*(csgn(I*x*(3+x))-1))-5)/ln(x+25))^3-I*Pi*x+3*x

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maxima [A]  time = 0.57, size = 37, normalized size = 1.23 \begin {gather*} -x \log \left (-\log \left (x + 25\right ) \log \left (-\log \relax (3) + \log \relax (x) + \log \left (-x - 3\right )\right ) + 5\right ) + x \log \left (\log \left (x + 25\right )\right ) + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-28*x-75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(5*x^2+140*x+375)*log(-1/3*x^2-x)*
log(x+25))*log((-log(x+25)*log(log(-1/3*x^2-x))+5)/log(x+25))+(3*x^2+84*x+225)*log(-1/3*x^2-x)*log(x+25)^2*log
(log(-1/3*x^2-x))+(-2*x^2-53*x-75)*log(x+25)^2+(-15*x^2-420*x-1125)*log(-1/3*x^2-x)*log(x+25)+(-5*x^2-15*x)*lo
g(-1/3*x^2-x))/((x^2+28*x+75)*log(-1/3*x^2-x)*log(x+25)^2*log(log(-1/3*x^2-x))+(-5*x^2-140*x-375)*log(-1/3*x^2
-x)*log(x+25)),x, algorithm="maxima")

[Out]

-x*log(-log(x + 25)*log(-log(3) + log(x) + log(-x - 3)) + 5) + x*log(log(x + 25)) + 3*x

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mupad [B]  time = 6.62, size = 32, normalized size = 1.07 \begin {gather*} -x\,\left (\ln \left (-\frac {\ln \left (x+25\right )\,\ln \left (\ln \left (-\frac {x^2}{3}-x\right )\right )-5}{\ln \left (x+25\right )}\right )-3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + 25)^2*(53*x + 2*x^2 + 75) - log(-(log(x + 25)*log(log(- x - x^2/3)) - 5)/log(x + 25))*(log(x + 25
)*log(- x - x^2/3)*(140*x + 5*x^2 + 375) - log(x + 25)^2*log(log(- x - x^2/3))*log(- x - x^2/3)*(28*x + x^2 +
75)) + log(- x - x^2/3)*(15*x + 5*x^2) + log(x + 25)*log(- x - x^2/3)*(420*x + 15*x^2 + 1125) - log(x + 25)^2*
log(log(- x - x^2/3))*log(- x - x^2/3)*(84*x + 3*x^2 + 225))/(log(x + 25)*log(- x - x^2/3)*(140*x + 5*x^2 + 37
5) - log(x + 25)^2*log(log(- x - x^2/3))*log(- x - x^2/3)*(28*x + x^2 + 75)),x)

[Out]

-x*(log(-(log(x + 25)*log(log(- x - x^2/3)) - 5)/log(x + 25)) - 3)

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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((((-x**2-28*x-75)*ln(-1/3*x**2-x)*ln(x+25)**2*ln(ln(-1/3*x**2-x))+(5*x**2+140*x+375)*ln(-1/3*x**2-x)
*ln(x+25))*ln((-ln(x+25)*ln(ln(-1/3*x**2-x))+5)/ln(x+25))+(3*x**2+84*x+225)*ln(-1/3*x**2-x)*ln(x+25)**2*ln(ln(
-1/3*x**2-x))+(-2*x**2-53*x-75)*ln(x+25)**2+(-15*x**2-420*x-1125)*ln(-1/3*x**2-x)*ln(x+25)+(-5*x**2-15*x)*ln(-
1/3*x**2-x))/((x**2+28*x+75)*ln(-1/3*x**2-x)*ln(x+25)**2*ln(ln(-1/3*x**2-x))+(-5*x**2-140*x-375)*ln(-1/3*x**2-
x)*ln(x+25)),x)

[Out]

Timed out

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