3.97.7 \(\int \frac {-2400 x+1200 x^2+(-3750+1875 x+4800 x^2-1800 x^3) \log (x)+(2400-1200 x+(-6000 x+2400 x^2) \log (x)) \log ((2-x) \log (x))+(1200-600 x) \log (x) \log ^2((2-x) \log (x))}{(-5000 x^2+2500 x^3+3200 x^4-1600 x^5-512 x^6+256 x^7) \log (x)+(-6400 x^3+3200 x^4+2048 x^5-1024 x^6) \log (x) \log ((2-x) \log (x))+(3200 x^2-1600 x^3-3072 x^4+1536 x^5) \log (x) \log ^2((2-x) \log (x))+(2048 x^3-1024 x^4) \log (x) \log ^3((2-x) \log (x))+(-512 x^2+256 x^3) \log (x) \log ^4((2-x) \log (x))} \, dx\)

Optimal. Leaf size=30 \[ \frac {3}{2 x \left (-2+\frac {16}{25} (x-\log ((2-x) \log (x)))^2\right )} \]

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Rubi [F]  time = 16.92, 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 {-2400 x+1200 x^2+\left (-3750+1875 x+4800 x^2-1800 x^3\right ) \log (x)+\left (2400-1200 x+\left (-6000 x+2400 x^2\right ) \log (x)\right ) \log ((2-x) \log (x))+(1200-600 x) \log (x) \log ^2((2-x) \log (x))}{\left (-5000 x^2+2500 x^3+3200 x^4-1600 x^5-512 x^6+256 x^7\right ) \log (x)+\left (-6400 x^3+3200 x^4+2048 x^5-1024 x^6\right ) \log (x) \log ((2-x) \log (x))+\left (3200 x^2-1600 x^3-3072 x^4+1536 x^5\right ) \log (x) \log ^2((2-x) \log (x))+\left (2048 x^3-1024 x^4\right ) \log (x) \log ^3((2-x) \log (x))+\left (-512 x^2+256 x^3\right ) \log (x) \log ^4((2-x) \log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2400*x + 1200*x^2 + (-3750 + 1875*x + 4800*x^2 - 1800*x^3)*Log[x] + (2400 - 1200*x + (-6000*x + 2400*x^2
)*Log[x])*Log[(2 - x)*Log[x]] + (1200 - 600*x)*Log[x]*Log[(2 - x)*Log[x]]^2)/((-5000*x^2 + 2500*x^3 + 3200*x^4
- 1600*x^5 - 512*x^6 + 256*x^7)*Log[x] + (-6400*x^3 + 3200*x^4 + 2048*x^5 - 1024*x^6)*Log[x]*Log[(2 - x)*Log[
x]] + (3200*x^2 - 1600*x^3 - 3072*x^4 + 1536*x^5)*Log[x]*Log[(2 - x)*Log[x]]^2 + (2048*x^3 - 1024*x^4)*Log[x]*
Log[(2 - x)*Log[x]]^3 + (-512*x^2 + 256*x^3)*Log[x]*Log[(2 - x)*Log[x]]^4),x]

[Out]

-300*Defer[Int][(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2)^(-2), x] + 300*Defe
r[Int][1/((-2 + x)*(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2)^2), x] + 300*Def
er[Int][1/(x*Log[x]*(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2)^2), x] - 150*De
fer[Int][Log[-((-2 + x)*Log[x])]/((-2 + x)*(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[
x])]^2)^2), x] + 450*Defer[Int][Log[-((-2 + x)*Log[x])]/(x*(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log
[-((-2 + x)*Log[x])]^2)^2), x] - 300*Defer[Int][Log[-((-2 + x)*Log[x])]/(x^2*Log[x]*(-25 + 8*x^2 - 16*x*Log[-(
(-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2)^2), x] - (75*Defer[Int][1/(x^2*(-25 + 8*x^2 - 16*x*Log[-((-2
+ x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2)), x])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {75 \left (-16 (-2+x) (x-\log (-((-2+x) \log (x))))+\log (x) \left (50-25 x-64 x^2+24 x^3+16 (5-2 x) x \log (-((-2+x) \log (x)))+8 (-2+x) \log ^2(-((-2+x) \log (x)))\right )\right )}{4 (2-x) x^2 \log (x) \left (25-8 x^2+16 x \log (-((-2+x) \log (x)))-8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx\\ &=\frac {75}{4} \int \frac {-16 (-2+x) (x-\log (-((-2+x) \log (x))))+\log (x) \left (50-25 x-64 x^2+24 x^3+16 (5-2 x) x \log (-((-2+x) \log (x)))+8 (-2+x) \log ^2(-((-2+x) \log (x)))\right )}{(2-x) x^2 \log (x) \left (25-8 x^2+16 x \log (-((-2+x) \log (x)))-8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx\\ &=\frac {75}{4} \int \left (-\frac {16 \left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{(-2+x) x^2 \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2}-\frac {1}{x^2 \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )}\right ) \, dx\\ &=-\left (\frac {75}{4} \int \frac {1}{x^2 \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )} \, dx\right )-300 \int \frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{(-2+x) x^2 \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx\\ &=-\left (\frac {75}{4} \int \frac {1}{x^2 \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )} \, dx\right )-300 \int \left (\frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{4 (-2+x) \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2}-\frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{2 x^2 \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2}-\frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{4 x \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2}\right ) \, dx\\ &=-\left (\frac {75}{4} \int \frac {1}{x^2 \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )} \, dx\right )-75 \int \frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{(-2+x) \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx+75 \int \frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{x \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx+150 \int \frac {\left (2-x-3 x \log (x)+x^2 \log (x)\right ) (x-\log (-((-2+x) \log (x))))}{x^2 \log (x) \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 39, normalized size = 1.30 \begin {gather*} \frac {75}{4 x \left (-25+8 x^2-16 x \log (-((-2+x) \log (x)))+8 \log ^2(-((-2+x) \log (x)))\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2400*x + 1200*x^2 + (-3750 + 1875*x + 4800*x^2 - 1800*x^3)*Log[x] + (2400 - 1200*x + (-6000*x + 24
00*x^2)*Log[x])*Log[(2 - x)*Log[x]] + (1200 - 600*x)*Log[x]*Log[(2 - x)*Log[x]]^2)/((-5000*x^2 + 2500*x^3 + 32
00*x^4 - 1600*x^5 - 512*x^6 + 256*x^7)*Log[x] + (-6400*x^3 + 3200*x^4 + 2048*x^5 - 1024*x^6)*Log[x]*Log[(2 - x
)*Log[x]] + (3200*x^2 - 1600*x^3 - 3072*x^4 + 1536*x^5)*Log[x]*Log[(2 - x)*Log[x]]^2 + (2048*x^3 - 1024*x^4)*L
og[x]*Log[(2 - x)*Log[x]]^3 + (-512*x^2 + 256*x^3)*Log[x]*Log[(2 - x)*Log[x]]^4),x]

[Out]

75/(4*x*(-25 + 8*x^2 - 16*x*Log[-((-2 + x)*Log[x])] + 8*Log[-((-2 + x)*Log[x])]^2))

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fricas [A]  time = 0.69, size = 39, normalized size = 1.30 \begin {gather*} \frac {75}{4 \, {\left (8 \, x^{3} - 16 \, x^{2} \log \left (-{\left (x - 2\right )} \log \relax (x)\right ) + 8 \, x \log \left (-{\left (x - 2\right )} \log \relax (x)\right )^{2} - 25 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-600*x+1200)*log(x)*log((2-x)*log(x))^2+((2400*x^2-6000*x)*log(x)-1200*x+2400)*log((2-x)*log(x))+(
-1800*x^3+4800*x^2+1875*x-3750)*log(x)+1200*x^2-2400*x)/((256*x^3-512*x^2)*log(x)*log((2-x)*log(x))^4+(-1024*x
^4+2048*x^3)*log(x)*log((2-x)*log(x))^3+(1536*x^5-3072*x^4-1600*x^3+3200*x^2)*log(x)*log((2-x)*log(x))^2+(-102
4*x^6+2048*x^5+3200*x^4-6400*x^3)*log(x)*log((2-x)*log(x))+(256*x^7-512*x^6-1600*x^5+3200*x^4+2500*x^3-5000*x^
2)*log(x)),x, algorithm="fricas")

[Out]

75/4/(8*x^3 - 16*x^2*log(-(x - 2)*log(x)) + 8*x*log(-(x - 2)*log(x))^2 - 25*x)

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giac [A]  time = 10.69, size = 45, normalized size = 1.50 \begin {gather*} \frac {75}{4 \, {\left (8 \, x^{3} - 16 \, x^{2} \log \left (-x \log \relax (x) + 2 \, \log \relax (x)\right ) + 8 \, x \log \left (-x \log \relax (x) + 2 \, \log \relax (x)\right )^{2} - 25 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-600*x+1200)*log(x)*log((2-x)*log(x))^2+((2400*x^2-6000*x)*log(x)-1200*x+2400)*log((2-x)*log(x))+(
-1800*x^3+4800*x^2+1875*x-3750)*log(x)+1200*x^2-2400*x)/((256*x^3-512*x^2)*log(x)*log((2-x)*log(x))^4+(-1024*x
^4+2048*x^3)*log(x)*log((2-x)*log(x))^3+(1536*x^5-3072*x^4-1600*x^3+3200*x^2)*log(x)*log((2-x)*log(x))^2+(-102
4*x^6+2048*x^5+3200*x^4-6400*x^3)*log(x)*log((2-x)*log(x))+(256*x^7-512*x^6-1600*x^5+3200*x^4+2500*x^3-5000*x^
2)*log(x)),x, algorithm="giac")

[Out]

75/4/(8*x^3 - 16*x^2*log(-x*log(x) + 2*log(x)) + 8*x*log(-x*log(x) + 2*log(x))^2 - 25*x)

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maple [C]  time = 5.57, size = 829, normalized size = 27.63

method	result	size
risch	\(-\frac {75}{4 x \left (25+8 \pi ^{2}+16 x \ln \left (\ln \relax (x )\right )-8 \ln \left (x -2\right )^{2}-8 \ln \left (\ln \relax (x )\right )^{2}-8 x^{2}+16 x \ln \left (x -2\right )-16 i \pi x \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )+2 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-4 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}-4 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}+8 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}-8 i \ln \left (\ln \relax (x )\right ) \pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}-8 i \ln \left (x -2\right ) \pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}+8 i \pi x \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}+16 i \ln \left (\ln \relax (x )\right ) \pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}+16 i \ln \left (x -2\right ) \pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}+8 i \pi x \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}+8 i \pi x \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 i \ln \left (x -2\right ) \pi \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 i \ln \left (x -2\right ) \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-16 \ln \left (\ln \relax (x )\right ) \ln \left (x -2\right )+8 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{3}-16 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}-8 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{5}+8 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{4}+2 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{6}-8 i \pi x \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )+8 i \ln \left (\ln \relax (x )\right ) \pi \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )+8 i \ln \left (x -2\right ) \pi \,\mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )+16 i \pi x -16 i \pi \ln \left (\ln \relax (x )\right )-16 i \pi \ln \left (x -2\right )-8 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{4}+4 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{5}+4 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{5}+8 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}+8 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{2}+2 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{4}+2 \pi ^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{4}-8 \pi ^{2} \mathrm {csgn}\left (i \left (x -2\right )\right ) \mathrm {csgn}\left (i \ln \relax (x ) \left (x -2\right )\right )^{4}\right )}\)	\(829\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-600*x+1200)*ln(x)*ln((2-x)*ln(x))^2+((2400*x^2-6000*x)*ln(x)-1200*x+2400)*ln((2-x)*ln(x))+(-1800*x^3+48
00*x^2+1875*x-3750)*ln(x)+1200*x^2-2400*x)/((256*x^3-512*x^2)*ln(x)*ln((2-x)*ln(x))^4+(-1024*x^4+2048*x^3)*ln(
x)*ln((2-x)*ln(x))^3+(1536*x^5-3072*x^4-1600*x^3+3200*x^2)*ln(x)*ln((2-x)*ln(x))^2+(-1024*x^6+2048*x^5+3200*x^
4-6400*x^3)*ln(x)*ln((2-x)*ln(x))+(256*x^7-512*x^6-1600*x^5+3200*x^4+2500*x^3-5000*x^2)*ln(x)),x,method=_RETUR
NVERBOSE)

[Out]

-75/4/x/(25+8*Pi^2+16*x*ln(ln(x))-8*ln(x-2)^2-8*ln(ln(x))^2-8*x^2+16*x*ln(x-2)+16*I*ln(ln(x))*Pi*csgn(I*ln(x)*
(x-2))^2+16*I*ln(x-2)*Pi*csgn(I*ln(x)*(x-2))^2-16*I*Pi*x*csgn(I*ln(x)*(x-2))^2-8*Pi^2*csgn(I*(x-2))*csgn(I*ln(
x))*csgn(I*ln(x)*(x-2))+2*Pi^2*csgn(I*(x-2))^2*csgn(I*ln(x))^2*csgn(I*ln(x)*(x-2))^2-4*Pi^2*csgn(I*(x-2))^2*cs
gn(I*ln(x))*csgn(I*ln(x)*(x-2))^3-4*Pi^2*csgn(I*(x-2))*csgn(I*ln(x))^2*csgn(I*ln(x)*(x-2))^3+8*Pi^2*csgn(I*ln(
x)*(x-2))^3+8*Pi^2*csgn(I*(x-2))*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))^3+16*I*Pi*x-16*I*Pi*ln(ln(x))-16*I*Pi*ln(x-
2)+8*I*Pi*x*csgn(I*(x-2))*csgn(I*ln(x)*(x-2))^2-16*Pi^2*csgn(I*ln(x)*(x-2))^2-8*I*ln(ln(x))*Pi*csgn(I*ln(x)*(x
-2))^3-8*I*ln(x-2)*Pi*csgn(I*ln(x)*(x-2))^3+8*I*Pi*x*csgn(I*ln(x)*(x-2))^3+8*I*Pi*x*csgn(I*ln(x))*csgn(I*ln(x)
*(x-2))^2-8*I*ln(ln(x))*Pi*csgn(I*(x-2))*csgn(I*ln(x)*(x-2))^2-8*I*ln(ln(x))*Pi*csgn(I*ln(x))*csgn(I*ln(x)*(x-
2))^2-8*I*ln(x-2)*Pi*csgn(I*(x-2))*csgn(I*ln(x)*(x-2))^2-8*I*ln(x-2)*Pi*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))^2-16
*ln(ln(x))*ln(x-2)-8*Pi^2*csgn(I*ln(x)*(x-2))^5+8*Pi^2*csgn(I*ln(x)*(x-2))^4+2*Pi^2*csgn(I*ln(x)*(x-2))^6-8*I*
Pi*x*csgn(I*(x-2))*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))+8*I*ln(ln(x))*Pi*csgn(I*(x-2))*csgn(I*ln(x))*csgn(I*ln(x)
*(x-2))+8*I*ln(x-2)*Pi*csgn(I*(x-2))*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))-8*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)*(x-2)
)^4+4*Pi^2*csgn(I*(x-2))*csgn(I*ln(x)*(x-2))^5+4*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))^5+8*Pi^2*csgn(I*(x-2))
*csgn(I*ln(x)*(x-2))^2+8*Pi^2*csgn(I*ln(x))*csgn(I*ln(x)*(x-2))^2+2*Pi^2*csgn(I*(x-2))^2*csgn(I*ln(x)*(x-2))^4
+2*Pi^2*csgn(I*ln(x))^2*csgn(I*ln(x)*(x-2))^4-8*Pi^2*csgn(I*(x-2))*csgn(I*ln(x)*(x-2))^4)

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maxima [B]  time = 0.46, size = 58, normalized size = 1.93 \begin {gather*} \frac {75}{4 \, {\left (8 \, x^{3} + 8 \, x \log \left (-x + 2\right )^{2} - 16 \, x^{2} \log \left (\log \relax (x)\right ) + 8 \, x \log \left (\log \relax (x)\right )^{2} - 16 \, {\left (x^{2} - x \log \left (\log \relax (x)\right )\right )} \log \left (-x + 2\right ) - 25 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-600*x+1200)*log(x)*log((2-x)*log(x))^2+((2400*x^2-6000*x)*log(x)-1200*x+2400)*log((2-x)*log(x))+(
-1800*x^3+4800*x^2+1875*x-3750)*log(x)+1200*x^2-2400*x)/((256*x^3-512*x^2)*log(x)*log((2-x)*log(x))^4+(-1024*x
^4+2048*x^3)*log(x)*log((2-x)*log(x))^3+(1536*x^5-3072*x^4-1600*x^3+3200*x^2)*log(x)*log((2-x)*log(x))^2+(-102
4*x^6+2048*x^5+3200*x^4-6400*x^3)*log(x)*log((2-x)*log(x))+(256*x^7-512*x^6-1600*x^5+3200*x^4+2500*x^3-5000*x^
2)*log(x)),x, algorithm="maxima")

[Out]

75/4/(8*x^3 + 8*x*log(-x + 2)^2 - 16*x^2*log(log(x)) + 8*x*log(log(x))^2 - 16*(x^2 - x*log(log(x)))*log(-x + 2
) - 25*x)

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mupad [B]  time = 6.16, size = 270, normalized size = 9.00 \begin {gather*} -\frac {300\,x^2\,{\ln \relax (x)}^2+\frac {75\,x^8\,{\ln \relax (x)}^4}{4}-x^5\,\left (1125\,{\ln \relax (x)}^4+1125\,{\ln \relax (x)}^3+150\,{\ln \relax (x)}^2\right )+x^4\,\left (675\,{\ln \relax (x)}^4+1650\,{\ln \relax (x)}^3+450\,{\ln \relax (x)}^2\right )+x^6\,\left (\frac {2775\,{\ln \relax (x)}^4}{4}+\frac {675\,{\ln \relax (x)}^3}{2}+\frac {75\,{\ln \relax (x)}^2}{4}\right )-x^7\,\left (\frac {375\,{\ln \relax (x)}^4}{2}+\frac {75\,{\ln \relax (x)}^3}{2}\right )-x^3\,\left (900\,{\ln \relax (x)}^3+600\,{\ln \relax (x)}^2\right )}{x^2\,\ln \relax (x)\,\left (x-2\right )\,\left (-8\,x^2+16\,x\,\ln \left (-\ln \relax (x)\,\left (x-2\right )\right )-8\,{\ln \left (-\ln \relax (x)\,\left (x-2\right )\right )}^2+25\right )\,\left (x^6\,{\ln \relax (x)}^3-8\,x^5\,{\ln \relax (x)}^3-2\,x^5\,{\ln \relax (x)}^2+21\,x^4\,{\ln \relax (x)}^3+14\,x^4\,{\ln \relax (x)}^2+x^4\,\ln \relax (x)-18\,x^3\,{\ln \relax (x)}^3-32\,x^3\,{\ln \relax (x)}^2-6\,x^3\,\ln \relax (x)+24\,x^2\,{\ln \relax (x)}^2+12\,x^2\,\ln \relax (x)-8\,x\,\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2400*x + log(-log(x)*(x - 2))*(1200*x + log(x)*(6000*x - 2400*x^2) - 2400) - 1200*x^2 - log(x)*(1875*x +
4800*x^2 - 1800*x^3 - 3750) + log(-log(x)*(x - 2))^2*log(x)*(600*x - 1200))/(log(x)*(5000*x^2 - 2500*x^3 - 320
0*x^4 + 1600*x^5 + 512*x^6 - 256*x^7) + log(-log(x)*(x - 2))*log(x)*(6400*x^3 - 3200*x^4 - 2048*x^5 + 1024*x^6
) - log(-log(x)*(x - 2))^2*log(x)*(3200*x^2 - 1600*x^3 - 3072*x^4 + 1536*x^5) + log(-log(x)*(x - 2))^4*log(x)*
(512*x^2 - 256*x^3) - log(-log(x)*(x - 2))^3*log(x)*(2048*x^3 - 1024*x^4)),x)

[Out]

-(300*x^2*log(x)^2 + (75*x^8*log(x)^4)/4 - x^5*(150*log(x)^2 + 1125*log(x)^3 + 1125*log(x)^4) + x^4*(450*log(x
)^2 + 1650*log(x)^3 + 675*log(x)^4) + x^6*((75*log(x)^2)/4 + (675*log(x)^3)/2 + (2775*log(x)^4)/4) - x^7*((75*
log(x)^3)/2 + (375*log(x)^4)/2) - x^3*(600*log(x)^2 + 900*log(x)^3))/(x^2*log(x)*(x - 2)*(16*x*log(-log(x)*(x
- 2)) - 8*x^2 - 8*log(-log(x)*(x - 2))^2 + 25)*(12*x^2*log(x) - 6*x^3*log(x) + x^4*log(x) + 24*x^2*log(x)^2 -
32*x^3*log(x)^2 - 18*x^3*log(x)^3 + 14*x^4*log(x)^2 + 21*x^4*log(x)^3 - 2*x^5*log(x)^2 - 8*x^5*log(x)^3 + x^6*
log(x)^3 - 8*x*log(x)))

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sympy [A]  time = 0.52, size = 36, normalized size = 1.20 \begin {gather*} \frac {75}{32 x^{3} - 64 x^{2} \log {\left (\left (2 - x\right ) \log {\relax (x )} \right )} + 32 x \log {\left (\left (2 - x\right ) \log {\relax (x )} \right )}^{2} - 100 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-600*x+1200)*ln(x)*ln((2-x)*ln(x))**2+((2400*x**2-6000*x)*ln(x)-1200*x+2400)*ln((2-x)*ln(x))+(-180
0*x**3+4800*x**2+1875*x-3750)*ln(x)+1200*x**2-2400*x)/((256*x**3-512*x**2)*ln(x)*ln((2-x)*ln(x))**4+(-1024*x**
4+2048*x**3)*ln(x)*ln((2-x)*ln(x))**3+(1536*x**5-3072*x**4-1600*x**3+3200*x**2)*ln(x)*ln((2-x)*ln(x))**2+(-102
4*x**6+2048*x**5+3200*x**4-6400*x**3)*ln(x)*ln((2-x)*ln(x))+(256*x**7-512*x**6-1600*x**5+3200*x**4+2500*x**3-5
000*x**2)*ln(x)),x)

[Out]

75/(32*x**3 - 64*x**2*log((2 - x)*log(x)) + 32*x*log((2 - x)*log(x))**2 - 100*x)

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