3.73.2 \(\int \frac {3125-9395 x+1867 x^2+8632 x^3-6351 x^4+566 x^5+832 x^6-304 x^7+32 x^8+(6250-3125 x-5625 x^2+4750 x^3-200 x^4-864 x^5+304 x^6-32 x^7) \log (2+x)+(6250 x-9385 x^2+3749 x^3+1002 x^4-1200 x^5+336 x^6-32 x^7+(-6250+9375 x-3750 x^2-1000 x^3+1200 x^4-336 x^5+32 x^6) \log (2+x)) \log (\frac {625 x-1001 x^2+600 x^3-160 x^4+16 x^5+(-625+1000 x-600 x^2+160 x^3-16 x^4) \log (2+x)}{625-1000 x+600 x^2-160 x^3+16 x^4})}{-6250 x^2+9385 x^3-3749 x^4-1002 x^5+1200 x^6-336 x^7+32 x^8+(6250 x-9375 x^2+3750 x^3+1000 x^4-1200 x^5+336 x^6-32 x^7) \log (2+x)+(6250 x-9385 x^2+3749 x^3+1002 x^4-1200 x^5+336 x^6-32 x^7+(-6250+9375 x-3750 x^2-1000 x^3+1200 x^4-336 x^5+32 x^6) \log (2+x)) \log (\frac {625 x-1001 x^2+600 x^3-160 x^4+16 x^5+(-625+1000 x-600 x^2+160 x^3-16 x^4) \log (2+x)}{625-1000 x+600 x^2-160 x^3+16 x^4})} \, dx\)

Optimal. Leaf size=29 \[ 1+x+\log \left (-x+\log \left (x-\frac {x^2}{(5-2 x)^4}-\log (2+x)\right )\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3125 - 9395*x + 1867*x^2 + 8632*x^3 - 6351*x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + (6250 - 3125*x -
5625*x^2 + 4750*x^3 - 200*x^4 - 864*x^5 + 304*x^6 - 32*x^7)*Log[2 + x] + (6250*x - 9385*x^2 + 3749*x^3 + 1002*
x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 1200*x^4 - 336*x^5 + 32*x^6)*Log[2
+ x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 600*x^2 + 160*x^3 - 16*x^4)*Log[2
+ x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)])/(-6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*x^6 -
336*x^7 + 32*x^8 + (6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200*x^5 + 336*x^6 - 32*x^7)*Log[2 + x] + (6250*
x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 120
0*x^4 - 336*x^5 + 32*x^6)*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 60
0*x^2 + 160*x^3 - 16*x^4)*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)]),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [A]  time = 0.32, size = 44, normalized size = 1.52 \begin {gather*} x+\log \left (x-\log \left (\frac {x \left (625-1001 x+600 x^2-160 x^3+16 x^4\right )}{(5-2 x)^4}-\log (2+x)\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3125 - 9395*x + 1867*x^2 + 8632*x^3 - 6351*x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + (6250 - 312
5*x - 5625*x^2 + 4750*x^3 - 200*x^4 - 864*x^5 + 304*x^6 - 32*x^7)*Log[2 + x] + (6250*x - 9385*x^2 + 3749*x^3 +
1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3 + 1200*x^4 - 336*x^5 + 32*x^6)
*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*x - 600*x^2 + 160*x^3 - 16*x^4)
*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)])/(-6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*
x^6 - 336*x^7 + 32*x^8 + (6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200*x^5 + 336*x^6 - 32*x^7)*Log[2 + x] +
(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6 - 32*x^7 + (-6250 + 9375*x - 3750*x^2 - 1000*x^3
+ 1200*x^4 - 336*x^5 + 32*x^6)*Log[2 + x])*Log[(625*x - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5 + (-625 + 1000*
x - 600*x^2 + 160*x^3 - 16*x^4)*Log[2 + x])/(625 - 1000*x + 600*x^2 - 160*x^3 + 16*x^4)]),x]

[Out]

x + Log[x - Log[(x*(625 - 1001*x + 600*x^2 - 160*x^3 + 16*x^4))/(5 - 2*x)^4 - Log[2 + x]]]

________________________________________________________________________________________

fricas [B]  time = 0.57, size = 81, normalized size = 2.79 \begin {gather*} x + \log \left (-x + \log \left (\frac {16 \, x^{5} - 160 \, x^{4} + 600 \, x^{3} - 1001 \, x^{2} - {\left (16 \, x^{4} - 160 \, x^{3} + 600 \, x^{2} - 1000 \, x + 625\right )} \log \left (x + 2\right ) + 625 \, x}{16 \, x^{4} - 160 \, x^{3} + 600 \, x^{2} - 1000 \, x + 625}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="fricas")

[Out]

x + log(-x + log((16*x^5 - 160*x^4 + 600*x^3 - 1001*x^2 - (16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625)*log(x +
2) + 625*x)/(16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625)))

________________________________________________________________________________________

giac [B]  time = 3.37, size = 93, normalized size = 3.21 \begin {gather*} x + \log \left (x - \log \left (16 \, x^{5} - 16 \, x^{4} \log \left (x + 2\right ) - 160 \, x^{4} + 160 \, x^{3} \log \left (x + 2\right ) + 600 \, x^{3} - 600 \, x^{2} \log \left (x + 2\right ) - 1001 \, x^{2} + 1000 \, x \log \left (x + 2\right ) + 625 \, x - 625 \, \log \left (x + 2\right )\right ) + \log \left (16 \, x^{4} - 160 \, x^{3} + 600 \, x^{2} - 1000 \, x + 625\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="giac")

[Out]

x + log(x - log(16*x^5 - 16*x^4*log(x + 2) - 160*x^4 + 160*x^3*log(x + 2) + 600*x^3 - 600*x^2*log(x + 2) - 100
1*x^2 + 1000*x*log(x + 2) + 625*x - 625*log(x + 2)) + log(16*x^4 - 160*x^3 + 600*x^2 - 1000*x + 625))

________________________________________________________________________________________

maple [C]  time = 0.35, size = 751, normalized size = 25.90

method	result	size
risch	\(x +\ln \left (\ln \left (x^{5}+\left (-\ln \left (2+x \right )-10\right ) x^{4}+\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}+\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}+\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x -\frac {625 \ln \left (2+x \right )}{16}\right )-\frac {i \left (\pi \,\mathrm {csgn}\left (\frac {i}{\left (x -\frac {5}{2}\right )^{4}}\right ) \mathrm {csgn}\left (i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )}{\left (x -\frac {5}{2}\right )^{4}}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{\left (x -\frac {5}{2}\right )^{4}}\right ) \mathrm {csgn}\left (\frac {i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )}{\left (x -\frac {5}{2}\right )^{4}}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right )^{2} \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{2}\right )+2 \pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{2}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{2}\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right )+\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{4}\right )+\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{4}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{2}\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{2}\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{3}\right ) \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{4}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x -\frac {5}{2}\right )^{4}\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )}{\left (x -\frac {5}{2}\right )^{4}}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i \left (-x^{5}-\left (-\ln \left (2+x \right )-10\right ) x^{4}-\left (10 \ln \left (2+x \right )+\frac {75}{2}\right ) x^{3}-\left (-\frac {75 \ln \left (2+x \right )}{2}-\frac {1001}{16}\right ) x^{2}-\left (\frac {125 \ln \left (2+x \right )}{2}+\frac {625}{16}\right ) x +\frac {625 \ln \left (2+x \right )}{16}\right )}{\left (x -\frac {5}{2}\right )^{4}}\right )^{3}-8 i \ln \left (x -\frac {5}{2}\right )-2 i x \right )}{2}\right )\)	\(751\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*ln(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^
3-9385*x^2+6250*x)*ln(((-16*x^4+160*x^3-600*x^2+1000*x-625)*ln(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16
*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*ln(2+x)+32*x
^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^
2+9375*x-6250)*ln(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*ln(((-16*x^4+160*x^3-600*x^2
+1000*x-625)*ln(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+336*
x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*ln(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^4+9385*x^3-625
0*x^2),x,method=_RETURNVERBOSE)

[Out]

x+ln(ln(x^5+(-ln(2+x)-10)*x^4+(10*ln(2+x)+75/2)*x^3+(-75/2*ln(2+x)-1001/16)*x^2+(125/2*ln(2+x)+625/16)*x-625/1
6*ln(2+x))-1/2*I*(Pi*csgn(I/(x-5/2)^4)*csgn(I*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-100
1/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)
*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))-Pi*csgn(I/(x-5/2)^4)*csgn(I/(x-5/2)
^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*l
n(2+x)))^2-Pi*csgn(I*(x-5/2))^2*csgn(I*(x-5/2)^2)+2*Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^2)^2-Pi*csgn(I*(x-5/2))*
csgn(I*(x-5/2)^2)*csgn(I*(x-5/2)^3)+Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^3)^2-Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^3
)*csgn(I*(x-5/2)^4)+Pi*csgn(I*(x-5/2))*csgn(I*(x-5/2)^4)^2-Pi*csgn(I*(x-5/2)^2)^3+Pi*csgn(I*(x-5/2)^2)*csgn(I*
(x-5/2)^3)^2-Pi*csgn(I*(x-5/2)^3)^3+Pi*csgn(I*(x-5/2)^3)*csgn(I*(x-5/2)^4)^2-Pi*csgn(I*(x-5/2)^4)^3+Pi*csgn(I*
(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2
+x)))*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x)-1001/16)*x^2-(125/2*ln(2+x
)+625/16)*x+625/16*ln(2+x)))^2-Pi*csgn(I/(x-5/2)^4*(-x^5-(-ln(2+x)-10)*x^4-(10*ln(2+x)+75/2)*x^3-(-75/2*ln(2+x
)-1001/16)*x^2-(125/2*ln(2+x)+625/16)*x+625/16*ln(2+x)))^3-8*I*ln(x-5/2)-2*I*x))

________________________________________________________________________________________

maxima [B]  time = 0.73, size = 76, normalized size = 2.62 \begin {gather*} x + \log \left (-x + \log \left (16 \, x^{5} - 16 \, x^{4} {\left (\log \left (x + 2\right ) + 10\right )} + 40 \, x^{3} {\left (4 \, \log \left (x + 2\right ) + 15\right )} - x^{2} {\left (600 \, \log \left (x + 2\right ) + 1001\right )} + 125 \, x {\left (8 \, \log \left (x + 2\right ) + 5\right )} - 625 \, \log \left (x + 2\right )\right ) - 4 \, \log \left (2 \, x - 5\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x^6-336*x^5+1200*x^4-1000*x^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+
3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+6
25*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+(-32*x^7+304*x^6-864*x^5-200*x^4+4750*x^3-5625*x^2-3125*x+6250)*log
(2+x)+32*x^8-304*x^7+832*x^6+566*x^5-6351*x^4+8632*x^3+1867*x^2-9395*x+3125)/(((32*x^6-336*x^5+1200*x^4-1000*x
^3-3750*x^2+9375*x-6250)*log(2+x)-32*x^7+336*x^6-1200*x^5+1002*x^4+3749*x^3-9385*x^2+6250*x)*log(((-16*x^4+160
*x^3-600*x^2+1000*x-625)*log(2+x)+16*x^5-160*x^4+600*x^3-1001*x^2+625*x)/(16*x^4-160*x^3+600*x^2-1000*x+625))+
(-32*x^7+336*x^6-1200*x^5+1000*x^4+3750*x^3-9375*x^2+6250*x)*log(2+x)+32*x^8-336*x^7+1200*x^6-1002*x^5-3749*x^
4+9385*x^3-6250*x^2),x, algorithm="maxima")

[Out]

x + log(-x + log(16*x^5 - 16*x^4*(log(x + 2) + 10) + 40*x^3*(4*log(x + 2) + 15) - x^2*(600*log(x + 2) + 1001)
+ 125*x*(8*log(x + 2) + 5) - 625*log(x + 2)) - 4*log(2*x - 5))

________________________________________________________________________________________

mupad [B]  time = 5.16, size = 53, normalized size = 1.83 \begin {gather*} x+\ln \left (x-\ln \left (\frac {625\,x-\ln \left (x+2\right )\,{\left (2\,x-5\right )}^4-1001\,x^2+600\,x^3-160\,x^4+16\,x^5}{{\left (2\,x-5\right )}^4}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((625*x - log(x + 2)*(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625) - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x
^5)/(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625))*(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^4 - 1200*x^5 + 336*x^6
- 32*x^7 - log(x + 2)*(3750*x^2 - 9375*x + 1000*x^3 - 1200*x^4 + 336*x^5 - 32*x^6 + 6250)) - log(x + 2)*(3125
*x + 5625*x^2 - 4750*x^3 + 200*x^4 + 864*x^5 - 304*x^6 + 32*x^7 - 6250) - 9395*x + 1867*x^2 + 8632*x^3 - 6351*
x^4 + 566*x^5 + 832*x^6 - 304*x^7 + 32*x^8 + 3125)/(log(x + 2)*(6250*x - 9375*x^2 + 3750*x^3 + 1000*x^4 - 1200
*x^5 + 336*x^6 - 32*x^7) + log((625*x - log(x + 2)*(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625) - 1001*x^2 + 60
0*x^3 - 160*x^4 + 16*x^5)/(600*x^2 - 1000*x - 160*x^3 + 16*x^4 + 625))*(6250*x - 9385*x^2 + 3749*x^3 + 1002*x^
4 - 1200*x^5 + 336*x^6 - 32*x^7 - log(x + 2)*(3750*x^2 - 9375*x + 1000*x^3 - 1200*x^4 + 336*x^5 - 32*x^6 + 625
0)) - 6250*x^2 + 9385*x^3 - 3749*x^4 - 1002*x^5 + 1200*x^6 - 336*x^7 + 32*x^8),x)

[Out]

x + log(x - log((625*x - log(x + 2)*(2*x - 5)^4 - 1001*x^2 + 600*x^3 - 160*x^4 + 16*x^5)/(2*x - 5)^4))

________________________________________________________________________________________

sympy [B]  time = 5.16, size = 75, normalized size = 2.59 \begin {gather*} x + \log {\left (- x + \log {\left (\frac {16 x^{5} - 160 x^{4} + 600 x^{3} - 1001 x^{2} + 625 x + \left (- 16 x^{4} + 160 x^{3} - 600 x^{2} + 1000 x - 625\right ) \log {\left (x + 2 \right )}}{16 x^{4} - 160 x^{3} + 600 x^{2} - 1000 x + 625} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((32*x**6-336*x**5+1200*x**4-1000*x**3-3750*x**2+9375*x-6250)*ln(2+x)-32*x**7+336*x**6-1200*x**5+10
02*x**4+3749*x**3-9385*x**2+6250*x)*ln(((-16*x**4+160*x**3-600*x**2+1000*x-625)*ln(2+x)+16*x**5-160*x**4+600*x
**3-1001*x**2+625*x)/(16*x**4-160*x**3+600*x**2-1000*x+625))+(-32*x**7+304*x**6-864*x**5-200*x**4+4750*x**3-56
25*x**2-3125*x+6250)*ln(2+x)+32*x**8-304*x**7+832*x**6+566*x**5-6351*x**4+8632*x**3+1867*x**2-9395*x+3125)/(((
32*x**6-336*x**5+1200*x**4-1000*x**3-3750*x**2+9375*x-6250)*ln(2+x)-32*x**7+336*x**6-1200*x**5+1002*x**4+3749*
x**3-9385*x**2+6250*x)*ln(((-16*x**4+160*x**3-600*x**2+1000*x-625)*ln(2+x)+16*x**5-160*x**4+600*x**3-1001*x**2
+625*x)/(16*x**4-160*x**3+600*x**2-1000*x+625))+(-32*x**7+336*x**6-1200*x**5+1000*x**4+3750*x**3-9375*x**2+625
0*x)*ln(2+x)+32*x**8-336*x**7+1200*x**6-1002*x**5-3749*x**4+9385*x**3-6250*x**2),x)

[Out]

x + log(-x + log((16*x**5 - 160*x**4 + 600*x**3 - 1001*x**2 + 625*x + (-16*x**4 + 160*x**3 - 600*x**2 + 1000*x
- 625)*log(x + 2))/(16*x**4 - 160*x**3 + 600*x**2 - 1000*x + 625)))

________________________________________________________________________________________