3.27.60 \(\int \frac {(8 x^4-x^5-6 x^6-x^7+(8 x^3-4 x^4-4 x^5) \log (3+x)+(-3 x^3+2 x^4+x^5) \log ^2(3+x)) \log ^3(-x+x^2)+e^{\frac {6}{x^2 \log ^2(-x+x^2)}} (-36+24 x+84 x^2+24 x^3+(-36-12 x+36 x^2+12 x^3) \log (-x+x^2)+(-3 x^3+2 x^4+x^5) \log ^3(-x+x^2))+e^{\frac {3}{x^2 \log ^2(-x+x^2)}} (36 x-24 x^2-84 x^3-24 x^4+(36-24 x-84 x^2-24 x^3) \log (3+x)+(36 x+12 x^2-36 x^3-12 x^4+(36+12 x-36 x^2-12 x^3) \log (3+x)) \log (-x+x^2)+(-8 x^3+4 x^4+4 x^5+(6 x^3-4 x^4-2 x^5) \log (3+x)) \log ^3(-x+x^2))}{(-3 x^3-4 x^4+2 x^5+4 x^6+x^7) \log ^3(-x+x^2)} \, dx\)

Optimal. Leaf size=35 \[ \frac {\left (-e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}}+x+\log (3+x)\right )^2}{-1-x} \]

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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[((8*x^4 - x^5 - 6*x^6 - x^7 + (8*x^3 - 4*x^4 - 4*x^5)*Log[3 + x] + (-3*x^3 + 2*x^4 + x^5)*Log[3 + x]^2)*Lo
g[-x + x^2]^3 + E^(6/(x^2*Log[-x + x^2]^2))*(-36 + 24*x + 84*x^2 + 24*x^3 + (-36 - 12*x + 36*x^2 + 12*x^3)*Log
[-x + x^2] + (-3*x^3 + 2*x^4 + x^5)*Log[-x + x^2]^3) + E^(3/(x^2*Log[-x + x^2]^2))*(36*x - 24*x^2 - 84*x^3 - 2
4*x^4 + (36 - 24*x - 84*x^2 - 24*x^3)*Log[3 + x] + (36*x + 12*x^2 - 36*x^3 - 12*x^4 + (36 + 12*x - 36*x^2 - 12
*x^3)*Log[3 + x])*Log[-x + x^2] + (-8*x^3 + 4*x^4 + 4*x^5 + (6*x^3 - 4*x^4 - 2*x^5)*Log[3 + x])*Log[-x + x^2]^
3))/((-3*x^3 - 4*x^4 + 2*x^5 + 4*x^6 + x^7)*Log[-x + x^2]^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.39, size = 77, normalized size = 2.20 \begin {gather*} -\frac {1+e^{\frac {6}{x^2 \log ^2((-1+x) x)}}+x-2 e^{\frac {3}{x^2 \log ^2((-1+x) x)}} x+x^2-2 \left (e^{\frac {3}{x^2 \log ^2((-1+x) x)}}-x\right ) \log (3+x)+\log ^2(3+x)}{1+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((8*x^4 - x^5 - 6*x^6 - x^7 + (8*x^3 - 4*x^4 - 4*x^5)*Log[3 + x] + (-3*x^3 + 2*x^4 + x^5)*Log[3 + x]
^2)*Log[-x + x^2]^3 + E^(6/(x^2*Log[-x + x^2]^2))*(-36 + 24*x + 84*x^2 + 24*x^3 + (-36 - 12*x + 36*x^2 + 12*x^
3)*Log[-x + x^2] + (-3*x^3 + 2*x^4 + x^5)*Log[-x + x^2]^3) + E^(3/(x^2*Log[-x + x^2]^2))*(36*x - 24*x^2 - 84*x
^3 - 24*x^4 + (36 - 24*x - 84*x^2 - 24*x^3)*Log[3 + x] + (36*x + 12*x^2 - 36*x^3 - 12*x^4 + (36 + 12*x - 36*x^
2 - 12*x^3)*Log[3 + x])*Log[-x + x^2] + (-8*x^3 + 4*x^4 + 4*x^5 + (6*x^3 - 4*x^4 - 2*x^5)*Log[3 + x])*Log[-x +
x^2]^3))/((-3*x^3 - 4*x^4 + 2*x^5 + 4*x^6 + x^7)*Log[-x + x^2]^3),x]

[Out]

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

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fricas [A]  time = 0.68, size = 66, normalized size = 1.89 \begin {gather*} -\frac {x^{2} - 2 \, {\left (x + \log \left (x + 3\right )\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} + x + e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 1}{x + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2-x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2
/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log
(3+x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x)-24*x^4-84*x^3-24*x^2+36*x)*exp(3
/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*log(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)
^3)/(x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="fricas")

[Out]

-(x^2 - 2*(x + log(x + 3))*e^(3/(x^2*log(x^2 - x)^2)) + 2*x*log(x + 3) + log(x + 3)^2 + x + e^(6/(x^2*log(x^2
- x)^2)) + 1)/(x + 1)

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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((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2-x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2
/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log
(3+x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x)-24*x^4-84*x^3-24*x^2+36*x)*exp(3
/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*log(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)
^3)/(x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="giac")

[Out]

undef

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maple [C]  time = 1.16, size = 242, normalized size = 6.91

method	result	size
risch	\(-\frac {2 x \ln \left (3+x \right )+x^{2}+\ln \left (3+x \right )^{2}+x +1}{x +1}-\frac {{\mathrm e}^{\frac {24}{x^{2} \left (-i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )-i \pi \,\mathrm {csgn}\left (i x \left (x -1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )+2 \ln \relax (x )+2 \ln \left (x -1\right )\right )^{2}}}}{x +1}+\frac {2 \left (\ln \left (3+x \right )+x \right ) {\mathrm e}^{\frac {12}{x^{2} \left (-i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )-i \pi \,\mathrm {csgn}\left (i x \left (x -1\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )+2 \ln \relax (x )+2 \ln \left (x -1\right )\right )^{2}}}}{x +1}\)	\(242\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^5+2*x^4-3*x^3)*ln(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*ln(x^2-x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2/ln(x^2-
x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*ln(3+x)+4*x^5+4*x^4-8*x^3)*ln(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*ln(3+x)-12*x^4
-36*x^3+12*x^2+36*x)*ln(x^2-x)+(-24*x^3-84*x^2-24*x+36)*ln(3+x)-24*x^4-84*x^3-24*x^2+36*x)*exp(3/x^2/ln(x^2-x)
^2)+((x^5+2*x^4-3*x^3)*ln(3+x)^2+(-4*x^5-4*x^4+8*x^3)*ln(3+x)-x^7-6*x^6-x^5+8*x^4)*ln(x^2-x)^3)/(x^7+4*x^6+2*x
^5-4*x^4-3*x^3)/ln(x^2-x)^3,x,method=_RETURNVERBOSE)

[Out]

-(2*x*ln(3+x)+x^2+ln(3+x)^2+x+1)/(x+1)-1/(x+1)*exp(24/x^2/(-I*Pi*csgn(I*x*(x-1))^3+I*Pi*csgn(I*x*(x-1))^2*csgn
(I*x)+I*Pi*csgn(I*x*(x-1))^2*csgn(I*(x-1))-I*Pi*csgn(I*x*(x-1))*csgn(I*x)*csgn(I*(x-1))+2*ln(x)+2*ln(x-1))^2)+
2*(ln(3+x)+x)/(x+1)*exp(12/x^2/(-I*Pi*csgn(I*x*(x-1))^3+I*Pi*csgn(I*x*(x-1))^2*csgn(I*x)+I*Pi*csgn(I*x*(x-1))^
2*csgn(I*(x-1))-I*Pi*csgn(I*x*(x-1))*csgn(I*x)*csgn(I*(x-1))+2*ln(x)+2*ln(x-1))^2)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {x^{2} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} + x + 1}{x + 1} + \int \frac {{\left ({\left (x^{4} - x^{3}\right )} \log \left (x - 1\right )^{3} + 3 \, {\left (x^{4} - x^{3}\right )} \log \left (x - 1\right )^{2} \log \relax (x) + {\left (x^{4} - x^{3}\right )} \log \relax (x)^{3} + 24 \, x^{2} + 3 \, {\left ({\left (x^{4} - x^{3}\right )} \log \relax (x)^{2} + 4 \, x^{2} - 4\right )} \log \left (x - 1\right ) + 12 \, {\left (x^{2} - 1\right )} \log \relax (x) + 12 \, x - 12\right )} e^{\left (\frac {6}{x^{2} \log \left (x - 1\right )^{2} + 2 \, x^{2} \log \left (x - 1\right ) \log \relax (x) + x^{2} \log \relax (x)^{2}}\right )}}{{\left (x^{6} + x^{5} - x^{4} - x^{3}\right )} \log \left (x - 1\right )^{3} + 3 \, {\left (x^{6} + x^{5} - x^{4} - x^{3}\right )} \log \left (x - 1\right )^{2} \log \relax (x) + 3 \, {\left (x^{6} + x^{5} - x^{4} - x^{3}\right )} \log \left (x - 1\right ) \log \relax (x)^{2} + {\left (x^{6} + x^{5} - x^{4} - x^{3}\right )} \log \relax (x)^{3}}\,{d x} - \int \frac {2 \, {\left (12 \, x^{4} - 2 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x - 1\right )^{3} - 6 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x - 1\right )^{2} \log \relax (x) - 2 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \relax (x)^{3} + 42 \, x^{3} + 12 \, x^{2} + {\left ({\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x - 1\right )^{3} + 3 \, {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x - 1\right )^{2} \log \relax (x) + {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \relax (x)^{3} + 12 \, x^{3} + 42 \, x^{2} + 3 \, {\left (2 \, x^{3} + {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \relax (x)^{2} + 6 \, x^{2} - 2 \, x - 6\right )} \log \left (x - 1\right ) + 6 \, {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \relax (x) + 12 \, x - 18\right )} \log \left (x + 3\right ) + 6 \, {\left (x^{4} + 3 \, x^{3} - {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \relax (x)^{2} - x^{2} - 3 \, x\right )} \log \left (x - 1\right ) + 6 \, {\left (x^{4} + 3 \, x^{3} - x^{2} - 3 \, x\right )} \log \relax (x) - 18 \, x\right )} e^{\left (\frac {3}{x^{2} \log \left (x - 1\right )^{2} + 2 \, x^{2} \log \left (x - 1\right ) \log \relax (x) + x^{2} \log \relax (x)^{2}}\right )}}{{\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x - 1\right )^{3} + 3 \, {\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x - 1\right )^{2} \log \relax (x) + 3 \, {\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x - 1\right ) \log \relax (x)^{2} + {\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \relax (x)^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2-x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2
/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log
(3+x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x)-24*x^4-84*x^3-24*x^2+36*x)*exp(3
/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*log(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)
^3)/(x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="maxima")

[Out]

-(x^2 + 2*x*log(x + 3) + log(x + 3)^2 + x + 1)/(x + 1) + integrate(((x^4 - x^3)*log(x - 1)^3 + 3*(x^4 - x^3)*l
og(x - 1)^2*log(x) + (x^4 - x^3)*log(x)^3 + 24*x^2 + 3*((x^4 - x^3)*log(x)^2 + 4*x^2 - 4)*log(x - 1) + 12*(x^2
- 1)*log(x) + 12*x - 12)*e^(6/(x^2*log(x - 1)^2 + 2*x^2*log(x - 1)*log(x) + x^2*log(x)^2))/((x^6 + x^5 - x^4
- x^3)*log(x - 1)^3 + 3*(x^6 + x^5 - x^4 - x^3)*log(x - 1)^2*log(x) + 3*(x^6 + x^5 - x^4 - x^3)*log(x - 1)*log
(x)^2 + (x^6 + x^5 - x^4 - x^3)*log(x)^3), x) - integrate(2*(12*x^4 - 2*(x^5 + x^4 - 2*x^3)*log(x - 1)^3 - 6*(
x^5 + x^4 - 2*x^3)*log(x - 1)^2*log(x) - 2*(x^5 + x^4 - 2*x^3)*log(x)^3 + 42*x^3 + 12*x^2 + ((x^5 + 2*x^4 - 3*
x^3)*log(x - 1)^3 + 3*(x^5 + 2*x^4 - 3*x^3)*log(x - 1)^2*log(x) + (x^5 + 2*x^4 - 3*x^3)*log(x)^3 + 12*x^3 + 42
*x^2 + 3*(2*x^3 + (x^5 + 2*x^4 - 3*x^3)*log(x)^2 + 6*x^2 - 2*x - 6)*log(x - 1) + 6*(x^3 + 3*x^2 - x - 3)*log(x
) + 12*x - 18)*log(x + 3) + 6*(x^4 + 3*x^3 - (x^5 + x^4 - 2*x^3)*log(x)^2 - x^2 - 3*x)*log(x - 1) + 6*(x^4 + 3
*x^3 - x^2 - 3*x)*log(x) - 18*x)*e^(3/(x^2*log(x - 1)^2 + 2*x^2*log(x - 1)*log(x) + x^2*log(x)^2))/((x^7 + 4*x
^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x - 1)^3 + 3*(x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x - 1)^2*log(x) + 3*(x^
7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x - 1)*log(x)^2 + (x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x)^3), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (4\,x^5+4\,x^4-8\,x^3\right )-{\ln \left (x+3\right )}^2\,\left (x^5+2\,x^4-3\,x^3\right )-8\,x^4+x^5+6\,x^6+x^7\right )-{\mathrm {e}}^{\frac {6}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (24\,x-\ln \left (x^2-x\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+84\,x^2+24\,x^3+{\ln \left (x^2-x\right )}^3\,\left (x^5+2\,x^4-3\,x^3\right )-36\right )+{\mathrm {e}}^{\frac {3}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (\ln \left (x+3\right )\,\left (24\,x^3+84\,x^2+24\,x-36\right )-36\,x+24\,x^2+84\,x^3+24\,x^4+{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (2\,x^5+4\,x^4-6\,x^3\right )+8\,x^3-4\,x^4-4\,x^5\right )-\ln \left (x^2-x\right )\,\left (36\,x+\ln \left (x+3\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+12\,x^2-36\,x^3-12\,x^4\right )\right )}{{\ln \left (x^2-x\right )}^3\,\left (x^7+4\,x^6+2\,x^5-4\,x^4-3\,x^3\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 8*x^3 + 4*x^5) - log(x + 3)^2*(2*x^4 - 3*x^3 + x^5) - 8*x^4 + x^5 +
6*x^6 + x^7) - exp(6/(x^2*log(x^2 - x)^2))*(24*x - log(x^2 - x)*(12*x - 36*x^2 - 12*x^3 + 36) + 84*x^2 + 24*x^
3 + log(x^2 - x)^3*(2*x^4 - 3*x^3 + x^5) - 36) + exp(3/(x^2*log(x^2 - x)^2))*(log(x + 3)*(24*x + 84*x^2 + 24*x
^3 - 36) - 36*x + 24*x^2 + 84*x^3 + 24*x^4 + log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 6*x^3 + 2*x^5) + 8*x^3 - 4*x^
4 - 4*x^5) - log(x^2 - x)*(36*x + log(x + 3)*(12*x - 36*x^2 - 12*x^3 + 36) + 12*x^2 - 36*x^3 - 12*x^4)))/(log(
x^2 - x)^3*(2*x^5 - 4*x^4 - 3*x^3 + 4*x^6 + x^7)),x)

[Out]

int(-(log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 8*x^3 + 4*x^5) - log(x + 3)^2*(2*x^4 - 3*x^3 + x^5) - 8*x^4 + x^5 +
6*x^6 + x^7) - exp(6/(x^2*log(x^2 - x)^2))*(24*x - log(x^2 - x)*(12*x - 36*x^2 - 12*x^3 + 36) + 84*x^2 + 24*x^
3 + log(x^2 - x)^3*(2*x^4 - 3*x^3 + x^5) - 36) + exp(3/(x^2*log(x^2 - x)^2))*(log(x + 3)*(24*x + 84*x^2 + 24*x
^3 - 36) - 36*x + 24*x^2 + 84*x^3 + 24*x^4 + log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 6*x^3 + 2*x^5) + 8*x^3 - 4*x^
4 - 4*x^5) - log(x^2 - x)*(36*x + log(x + 3)*(12*x - 36*x^2 - 12*x^3 + 36) + 12*x^2 - 36*x^3 - 12*x^4)))/(log(
x^2 - x)^3*(2*x^5 - 4*x^4 - 3*x^3 + 4*x^6 + x^7)), x)

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sympy [B]  time = 1.32, size = 100, normalized size = 2.86 \begin {gather*} - x + \frac {\left (- x - 1\right ) e^{\frac {6}{x^{2} \log {\left (x^{2} - x \right )}^{2}}} + \left (2 x^{2} + 2 x \log {\left (x + 3 \right )} + 2 x + 2 \log {\left (x + 3 \right )}\right ) e^{\frac {3}{x^{2} \log {\left (x^{2} - x \right )}^{2}}}}{x^{2} + 2 x + 1} - 2 \log {\left (x + 3 \right )} - \frac {\log {\left (x + 3 \right )}^{2}}{x + 1} + \frac {2 \log {\left (x + 3 \right )}}{x + 1} - \frac {1}{x + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**5+2*x**4-3*x**3)*ln(x**2-x)**3+(12*x**3+36*x**2-12*x-36)*ln(x**2-x)+24*x**3+84*x**2+24*x-36)*e
xp(3/x**2/ln(x**2-x)**2)**2+(((-2*x**5-4*x**4+6*x**3)*ln(3+x)+4*x**5+4*x**4-8*x**3)*ln(x**2-x)**3+((-12*x**3-3
6*x**2+12*x+36)*ln(3+x)-12*x**4-36*x**3+12*x**2+36*x)*ln(x**2-x)+(-24*x**3-84*x**2-24*x+36)*ln(3+x)-24*x**4-84
*x**3-24*x**2+36*x)*exp(3/x**2/ln(x**2-x)**2)+((x**5+2*x**4-3*x**3)*ln(3+x)**2+(-4*x**5-4*x**4+8*x**3)*ln(3+x)
-x**7-6*x**6-x**5+8*x**4)*ln(x**2-x)**3)/(x**7+4*x**6+2*x**5-4*x**4-3*x**3)/ln(x**2-x)**3,x)

[Out]

-x + ((-x - 1)*exp(6/(x**2*log(x**2 - x)**2)) + (2*x**2 + 2*x*log(x + 3) + 2*x + 2*log(x + 3))*exp(3/(x**2*log
(x**2 - x)**2)))/(x**2 + 2*x + 1) - 2*log(x + 3) - log(x + 3)**2/(x + 1) + 2*log(x + 3)/(x + 1) - 1/(x + 1)

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