3.92.38 \(\int \frac {-x+4 e^{60+4 x} x+16 x^2+64 x^4+e^{45+3 x} (8 x+24 x^2)+(4+16 x^2) \log (2)+e^{30+2 x} (4+48 x^2+48 x^3+4 x \log (2))+e^{15+x} (16 x+96 x^3+32 x^4+(8 x+8 x^2) \log (2))+(4+4 e^{30+2 x} x+16 x^2+e^{15+x} (8 x+8 x^2)) \log (3 x^2)}{e^{60+4 x} x-x^2+8 e^{45+3 x} x^2+16 x^5+8 x^3 \log (2)+x \log ^2(2)+e^{30+2 x} (24 x^3+2 x \log (2))+e^{15+x} (32 x^4+8 x^2 \log (2))+(2 e^{30+2 x} x+8 e^{15+x} x^2+8 x^3+2 x \log (2)) \log (3 x^2)+x \log ^2(3 x^2)} \, dx\)

Optimal. Leaf size=27 \[ \log \left (-x+\left (\left (e^{15+x}+2 x\right )^2+\log (2)+\log \left (3 x^2\right )\right )^2\right ) \]

________________________________________________________________________________________

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[(-x + 4*E^(60 + 4*x)*x + 16*x^2 + 64*x^4 + E^(45 + 3*x)*(8*x + 24*x^2) + (4 + 16*x^2)*Log[2] + E^(30 + 2*x
)*(4 + 48*x^2 + 48*x^3 + 4*x*Log[2]) + E^(15 + x)*(16*x + 96*x^3 + 32*x^4 + (8*x + 8*x^2)*Log[2]) + (4 + 4*E^(
30 + 2*x)*x + 16*x^2 + E^(15 + x)*(8*x + 8*x^2))*Log[3*x^2])/(E^(60 + 4*x)*x - x^2 + 8*E^(45 + 3*x)*x^2 + 16*x
^5 + 8*x^3*Log[2] + x*Log[2]^2 + E^(30 + 2*x)*(24*x^3 + 2*x*Log[2]) + E^(15 + x)*(32*x^4 + 8*x^2*Log[2]) + (2*
E^(30 + 2*x)*x + 8*E^(15 + x)*x^2 + 8*x^3 + 2*x*Log[2])*Log[3*x^2] + x*Log[3*x^2]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [F]  time = 1.64, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-x+4 e^{60+4 x} x+16 x^2+64 x^4+e^{45+3 x} \left (8 x+24 x^2\right )+\left (4+16 x^2\right ) \log (2)+e^{30+2 x} \left (4+48 x^2+48 x^3+4 x \log (2)\right )+e^{15+x} \left (16 x+96 x^3+32 x^4+\left (8 x+8 x^2\right ) \log (2)\right )+\left (4+4 e^{30+2 x} x+16 x^2+e^{15+x} \left (8 x+8 x^2\right )\right ) \log \left (3 x^2\right )}{e^{60+4 x} x-x^2+8 e^{45+3 x} x^2+16 x^5+8 x^3 \log (2)+x \log ^2(2)+e^{30+2 x} \left (24 x^3+2 x \log (2)\right )+e^{15+x} \left (32 x^4+8 x^2 \log (2)\right )+\left (2 e^{30+2 x} x+8 e^{15+x} x^2+8 x^3+2 x \log (2)\right ) \log \left (3 x^2\right )+x \log ^2\left (3 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-x + 4*E^(60 + 4*x)*x + 16*x^2 + 64*x^4 + E^(45 + 3*x)*(8*x + 24*x^2) + (4 + 16*x^2)*Log[2] + E^(30
+ 2*x)*(4 + 48*x^2 + 48*x^3 + 4*x*Log[2]) + E^(15 + x)*(16*x + 96*x^3 + 32*x^4 + (8*x + 8*x^2)*Log[2]) + (4 +
4*E^(30 + 2*x)*x + 16*x^2 + E^(15 + x)*(8*x + 8*x^2))*Log[3*x^2])/(E^(60 + 4*x)*x - x^2 + 8*E^(45 + 3*x)*x^2
+ 16*x^5 + 8*x^3*Log[2] + x*Log[2]^2 + E^(30 + 2*x)*(24*x^3 + 2*x*Log[2]) + E^(15 + x)*(32*x^4 + 8*x^2*Log[2])
+ (2*E^(30 + 2*x)*x + 8*E^(15 + x)*x^2 + 8*x^3 + 2*x*Log[2])*Log[3*x^2] + x*Log[3*x^2]^2),x]

[Out]

Integrate[(-x + 4*E^(60 + 4*x)*x + 16*x^2 + 64*x^4 + E^(45 + 3*x)*(8*x + 24*x^2) + (4 + 16*x^2)*Log[2] + E^(30
+ 2*x)*(4 + 48*x^2 + 48*x^3 + 4*x*Log[2]) + E^(15 + x)*(16*x + 96*x^3 + 32*x^4 + (8*x + 8*x^2)*Log[2]) + (4 +
4*E^(30 + 2*x)*x + 16*x^2 + E^(15 + x)*(8*x + 8*x^2))*Log[3*x^2])/(E^(60 + 4*x)*x - x^2 + 8*E^(45 + 3*x)*x^2
+ 16*x^5 + 8*x^3*Log[2] + x*Log[2]^2 + E^(30 + 2*x)*(24*x^3 + 2*x*Log[2]) + E^(15 + x)*(32*x^4 + 8*x^2*Log[2])
+ (2*E^(30 + 2*x)*x + 8*E^(15 + x)*x^2 + 8*x^3 + 2*x*Log[2])*Log[3*x^2] + x*Log[3*x^2]^2), x]

________________________________________________________________________________________

fricas [B]  time = 1.02, size = 105, normalized size = 3.89 \begin {gather*} \log \left (16 \, x^{4} + 8 \, x^{2} \log \relax (2) + 8 \, x e^{\left (3 \, x + 45\right )} + 2 \, {\left (12 \, x^{2} + \log \relax (2)\right )} e^{\left (2 \, x + 30\right )} + 8 \, {\left (4 \, x^{3} + x \log \relax (2)\right )} e^{\left (x + 15\right )} + \log \relax (2)^{2} + 2 \, {\left (4 \, x^{2} + 4 \, x e^{\left (x + 15\right )} + e^{\left (2 \, x + 30\right )} + \log \relax (2)\right )} \log \left (3 \, x^{2}\right ) + \log \left (3 \, x^{2}\right )^{2} - x + e^{\left (4 \, x + 60\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*exp(x+15)^2+(8*x^2+8*x)*exp(x+15)+16*x^2+4)*log(3*x^2)+4*x*exp(x+15)^4+(24*x^2+8*x)*exp(x+15)^
3+(4*x*log(2)+48*x^3+48*x^2+4)*exp(x+15)^2+((8*x^2+8*x)*log(2)+32*x^4+96*x^3+16*x)*exp(x+15)+(16*x^2+4)*log(2)
+64*x^4+16*x^2-x)/(x*log(3*x^2)^2+(2*x*exp(x+15)^2+8*x^2*exp(x+15)+2*x*log(2)+8*x^3)*log(3*x^2)+x*exp(x+15)^4+
8*x^2*exp(x+15)^3+(2*x*log(2)+24*x^3)*exp(x+15)^2+(8*x^2*log(2)+32*x^4)*exp(x+15)+x*log(2)^2+8*x^3*log(2)+16*x
^5-x^2),x, algorithm="fricas")

[Out]

log(16*x^4 + 8*x^2*log(2) + 8*x*e^(3*x + 45) + 2*(12*x^2 + log(2))*e^(2*x + 30) + 8*(4*x^3 + x*log(2))*e^(x +
15) + log(2)^2 + 2*(4*x^2 + 4*x*e^(x + 15) + e^(2*x + 30) + log(2))*log(3*x^2) + log(3*x^2)^2 - x + e^(4*x + 6
0))

________________________________________________________________________________________

giac [B]  time = 0.90, size = 173, normalized size = 6.41 \begin {gather*} \log \left (16 \, x^{4} + 32 \, x^{3} e^{\left (x + 15\right )} + 24 \, x^{2} e^{\left (2 \, x + 30\right )} + 8 \, x^{2} \log \relax (3) + 8 \, x e^{\left (x + 15\right )} \log \relax (3) + 8 \, x^{2} \log \relax (2) + 8 \, x e^{\left (x + 15\right )} \log \relax (2) + 16 \, x^{2} \log \left (x \mathrm {sgn}\relax (x)\right ) + 16 \, x e^{\left (x + 15\right )} \log \left (x \mathrm {sgn}\relax (x)\right ) + 8 \, x e^{\left (3 \, x + 45\right )} + 2 \, e^{\left (2 \, x + 30\right )} \log \relax (3) + \log \relax (3)^{2} + 2 \, e^{\left (2 \, x + 30\right )} \log \relax (2) + 2 \, \log \relax (3) \log \relax (2) + \log \relax (2)^{2} + 4 \, e^{\left (2 \, x + 30\right )} \log \left (x \mathrm {sgn}\relax (x)\right ) + 4 \, \log \relax (3) \log \left (x \mathrm {sgn}\relax (x)\right ) + 4 \, \log \relax (2) \log \left (x \mathrm {sgn}\relax (x)\right ) + 4 \, \log \left (x \mathrm {sgn}\relax (x)\right )^{2} - x + e^{\left (4 \, x + 60\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*exp(x+15)^2+(8*x^2+8*x)*exp(x+15)+16*x^2+4)*log(3*x^2)+4*x*exp(x+15)^4+(24*x^2+8*x)*exp(x+15)^
3+(4*x*log(2)+48*x^3+48*x^2+4)*exp(x+15)^2+((8*x^2+8*x)*log(2)+32*x^4+96*x^3+16*x)*exp(x+15)+(16*x^2+4)*log(2)
+64*x^4+16*x^2-x)/(x*log(3*x^2)^2+(2*x*exp(x+15)^2+8*x^2*exp(x+15)+2*x*log(2)+8*x^3)*log(3*x^2)+x*exp(x+15)^4+
8*x^2*exp(x+15)^3+(2*x*log(2)+24*x^3)*exp(x+15)^2+(8*x^2*log(2)+32*x^4)*exp(x+15)+x*log(2)^2+8*x^3*log(2)+16*x
^5-x^2),x, algorithm="giac")

[Out]

log(16*x^4 + 32*x^3*e^(x + 15) + 24*x^2*e^(2*x + 30) + 8*x^2*log(3) + 8*x*e^(x + 15)*log(3) + 8*x^2*log(2) + 8
*x*e^(x + 15)*log(2) + 16*x^2*log(x*sgn(x)) + 16*x*e^(x + 15)*log(x*sgn(x)) + 8*x*e^(3*x + 45) + 2*e^(2*x + 30
)*log(3) + log(3)^2 + 2*e^(2*x + 30)*log(2) + 2*log(3)*log(2) + log(2)^2 + 4*e^(2*x + 30)*log(x*sgn(x)) + 4*lo
g(3)*log(x*sgn(x)) + 4*log(2)*log(x*sgn(x)) + 4*log(x*sgn(x))^2 - x + e^(4*x + 60))

________________________________________________________________________________________

maple [C]  time = 0.35, size = 592, normalized size = 21.93

method	result	size
risch	\(\ln \left (-\frac {x}{4}+2 x^{2} \ln \relax (3)+\frac {\ln \relax (3)^{2}}{4}+\frac {\ln \relax (2)^{2}}{4}+\ln \relax (x )^{2}+4 x^{4}+2 x^{2} \ln \relax (2)-i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{2 x +30}}{4}-\frac {i \pi \ln \relax (2) \mathrm {csgn}\left (i x^{2}\right )^{3}}{4}-\frac {i \ln \relax (3) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{4}+\frac {\ln \relax (2) \ln \relax (3)}{2}+\frac {{\mathrm e}^{4 x +60}}{4}+6 \,{\mathrm e}^{2 x +30} x^{2}+\frac {\ln \relax (3) {\mathrm e}^{2 x +30}}{2}+\frac {\ln \relax (2) {\mathrm e}^{2 x +30}}{2}+2 \,{\mathrm e}^{3 x +45} x -i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x +15}+2 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x +15}+8 \,{\mathrm e}^{x +15} x^{3}-\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}}{16}+\left (4 x^{2}-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}}{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\ln \relax (3)+4 x \,{\mathrm e}^{x +15}+{\mathrm e}^{2 x +30}+\ln \relax (2)\right ) \ln \relax (x )+\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )}{4}-\frac {3 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}}{8}+\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}}{4}-\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}}{16}+2 \,{\mathrm e}^{x +15} \ln \relax (2) x -\frac {i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{2 x +30}}{4}+\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{2 x +30}}{2}+\frac {i \pi \ln \relax (2) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}}{2}-\frac {i \ln \relax (3) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{4}+\frac {i \ln \relax (3) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}}{2}-i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x +15}+2 \,{\mathrm e}^{x +15} \ln \relax (3) x -\frac {i \pi \ln \relax (2) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{4}-i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}\right )\)	\(592\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x*exp(x+15)^2+(8*x^2+8*x)*exp(x+15)+16*x^2+4)*ln(3*x^2)+4*x*exp(x+15)^4+(24*x^2+8*x)*exp(x+15)^3+(4*x*
ln(2)+48*x^3+48*x^2+4)*exp(x+15)^2+((8*x^2+8*x)*ln(2)+32*x^4+96*x^3+16*x)*exp(x+15)+(16*x^2+4)*ln(2)+64*x^4+16
*x^2-x)/(x*ln(3*x^2)^2+(2*x*exp(x+15)^2+8*x^2*exp(x+15)+2*x*ln(2)+8*x^3)*ln(3*x^2)+x*exp(x+15)^4+8*x^2*exp(x+1
5)^3+(2*x*ln(2)+24*x^3)*exp(x+15)^2+(8*x^2*ln(2)+32*x^4)*exp(x+15)+x*ln(2)^2+8*x^3*ln(2)+16*x^5-x^2),x,method=
_RETURNVERBOSE)

[Out]

ln(-1/4*x+2*x^2*ln(3)+1/4*ln(3)^2+1/4*ln(2)^2+ln(x)^2+4*x^4+2*x^2*ln(2)-1/4*I*Pi*csgn(I*x^2)^3*exp(2*x+30)-1/4
*I*Pi*ln(2)*csgn(I*x^2)^3-1/4*I*ln(3)*Pi*csgn(I*x^2)^3+1/2*ln(2)*ln(3)+1/4*exp(4*x+60)+6*exp(2*x+30)*x^2+1/2*l
n(3)*exp(2*x+30)+1/2*ln(2)*exp(2*x+30)+2*exp(3*x+45)*x+8*exp(x+15)*x^3-1/4*I*Pi*csgn(I*x)^2*csgn(I*x^2)*exp(2*
x+30)+1/2*I*Pi*csgn(I*x)*csgn(I*x^2)^2*exp(2*x+30)-I*Pi*x*csgn(I*x)^2*csgn(I*x^2)*exp(x+15)+2*I*Pi*x*csgn(I*x)
*csgn(I*x^2)^2*exp(x+15)+1/4*Pi^2*csgn(I*x^2)^5*csgn(I*x)-3/8*Pi^2*csgn(I*x^2)^4*csgn(I*x)^2+1/4*Pi^2*csgn(I*x
^2)^3*csgn(I*x)^3-1/16*Pi^2*csgn(I*x^2)^2*csgn(I*x)^4+1/2*I*Pi*ln(2)*csgn(I*x)*csgn(I*x^2)^2-1/4*I*ln(3)*Pi*cs
gn(I*x)^2*csgn(I*x^2)+1/2*I*ln(3)*Pi*csgn(I*x)*csgn(I*x^2)^2-1/16*Pi^2*csgn(I*x^2)^6+2*exp(x+15)*ln(2)*x+(4*x^
2-1/2*I*Pi*csgn(I*x^2)^3-1/2*I*Pi*csgn(I*x^2)*csgn(I*x)^2+I*Pi*csgn(I*x^2)^2*csgn(I*x)+ln(3)+4*x*exp(x+15)+exp
(2*x+30)+ln(2))*ln(x)-I*Pi*x^2*csgn(I*x^2)^3+2*exp(x+15)*ln(3)*x-I*Pi*x*csgn(I*x^2)^3*exp(x+15)-1/4*I*Pi*ln(2)
*csgn(I*x)^2*csgn(I*x^2)-I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2)

________________________________________________________________________________________

maxima [B]  time = 0.56, size = 128, normalized size = 4.74 \begin {gather*} \log \left ({\left (16 \, x^{4} + 8 \, x^{2} {\left (\log \relax (3) + \log \relax (2)\right )} + 2 \, {\left (12 \, x^{2} e^{30} + {\left (\log \relax (3) + \log \relax (2)\right )} e^{30} + 2 \, e^{30} \log \relax (x)\right )} e^{\left (2 \, x\right )} + 8 \, x e^{\left (3 \, x + 45\right )} + 8 \, {\left (4 \, x^{3} e^{15} + x {\left (\log \relax (3) + \log \relax (2)\right )} e^{15} + 2 \, x e^{15} \log \relax (x)\right )} e^{x} + \log \relax (3)^{2} + 2 \, \log \relax (3) \log \relax (2) + \log \relax (2)^{2} + 4 \, {\left (4 \, x^{2} + \log \relax (3) + \log \relax (2)\right )} \log \relax (x) + 4 \, \log \relax (x)^{2} - x + e^{\left (4 \, x + 60\right )}\right )} e^{\left (-60\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*exp(x+15)^2+(8*x^2+8*x)*exp(x+15)+16*x^2+4)*log(3*x^2)+4*x*exp(x+15)^4+(24*x^2+8*x)*exp(x+15)^
3+(4*x*log(2)+48*x^3+48*x^2+4)*exp(x+15)^2+((8*x^2+8*x)*log(2)+32*x^4+96*x^3+16*x)*exp(x+15)+(16*x^2+4)*log(2)
+64*x^4+16*x^2-x)/(x*log(3*x^2)^2+(2*x*exp(x+15)^2+8*x^2*exp(x+15)+2*x*log(2)+8*x^3)*log(3*x^2)+x*exp(x+15)^4+
8*x^2*exp(x+15)^3+(2*x*log(2)+24*x^3)*exp(x+15)^2+(8*x^2*log(2)+32*x^4)*exp(x+15)+x*log(2)^2+8*x^3*log(2)+16*x
^5-x^2),x, algorithm="maxima")

[Out]

log((16*x^4 + 8*x^2*(log(3) + log(2)) + 2*(12*x^2*e^30 + (log(3) + log(2))*e^30 + 2*e^30*log(x))*e^(2*x) + 8*x
*e^(3*x + 45) + 8*(4*x^3*e^15 + x*(log(3) + log(2))*e^15 + 2*x*e^15*log(x))*e^x + log(3)^2 + 2*log(3)*log(2) +
log(2)^2 + 4*(4*x^2 + log(3) + log(2))*log(x) + 4*log(x)^2 - x + e^(4*x + 60))*e^(-60))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x+30}\,\left (48\,x^3+48\,x^2+4\,\ln \relax (2)\,x+4\right )-x+\ln \left (3\,x^2\right )\,\left ({\mathrm {e}}^{x+15}\,\left (8\,x^2+8\,x\right )+4\,x\,{\mathrm {e}}^{2\,x+30}+16\,x^2+4\right )+\ln \relax (2)\,\left (16\,x^2+4\right )+{\mathrm {e}}^{3\,x+45}\,\left (24\,x^2+8\,x\right )+4\,x\,{\mathrm {e}}^{4\,x+60}+{\mathrm {e}}^{x+15}\,\left (16\,x+\ln \relax (2)\,\left (8\,x^2+8\,x\right )+96\,x^3+32\,x^4\right )+16\,x^2+64\,x^4}{x\,{\mathrm {e}}^{4\,x+60}+x\,{\ln \relax (2)}^2+8\,x^3\,\ln \relax (2)+\ln \left (3\,x^2\right )\,\left (2\,x\,\ln \relax (2)+2\,x\,{\mathrm {e}}^{2\,x+30}+8\,x^2\,{\mathrm {e}}^{x+15}+8\,x^3\right )+8\,x^2\,{\mathrm {e}}^{3\,x+45}+{\mathrm {e}}^{2\,x+30}\,\left (24\,x^3+2\,\ln \relax (2)\,x\right )+{\mathrm {e}}^{x+15}\,\left (32\,x^4+8\,\ln \relax (2)\,x^2\right )-x^2+16\,x^5+x\,{\ln \left (3\,x^2\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x + 30)*(4*x*log(2) + 48*x^2 + 48*x^3 + 4) - x + log(3*x^2)*(exp(x + 15)*(8*x + 8*x^2) + 4*x*exp(2*
x + 30) + 16*x^2 + 4) + log(2)*(16*x^2 + 4) + exp(3*x + 45)*(8*x + 24*x^2) + 4*x*exp(4*x + 60) + exp(x + 15)*(
16*x + log(2)*(8*x + 8*x^2) + 96*x^3 + 32*x^4) + 16*x^2 + 64*x^4)/(x*exp(4*x + 60) + x*log(2)^2 + 8*x^3*log(2)
+ log(3*x^2)*(2*x*log(2) + 2*x*exp(2*x + 30) + 8*x^2*exp(x + 15) + 8*x^3) + 8*x^2*exp(3*x + 45) + exp(2*x + 3
0)*(2*x*log(2) + 24*x^3) + exp(x + 15)*(8*x^2*log(2) + 32*x^4) - x^2 + 16*x^5 + x*log(3*x^2)^2),x)

[Out]

int((exp(2*x + 30)*(4*x*log(2) + 48*x^2 + 48*x^3 + 4) - x + log(3*x^2)*(exp(x + 15)*(8*x + 8*x^2) + 4*x*exp(2*
x + 30) + 16*x^2 + 4) + log(2)*(16*x^2 + 4) + exp(3*x + 45)*(8*x + 24*x^2) + 4*x*exp(4*x + 60) + exp(x + 15)*(
16*x + log(2)*(8*x + 8*x^2) + 96*x^3 + 32*x^4) + 16*x^2 + 64*x^4)/(x*exp(4*x + 60) + x*log(2)^2 + 8*x^3*log(2)
+ log(3*x^2)*(2*x*log(2) + 2*x*exp(2*x + 30) + 8*x^2*exp(x + 15) + 8*x^3) + 8*x^2*exp(3*x + 45) + exp(2*x + 3
0)*(2*x*log(2) + 24*x^3) + exp(x + 15)*(8*x^2*log(2) + 32*x^4) - x^2 + 16*x^5 + x*log(3*x^2)^2), x)

________________________________________________________________________________________

sympy [B]  time = 2.67, size = 122, normalized size = 4.52 \begin {gather*} \log {\left (16 x^{4} + 8 x^{2} \log {\left (3 x^{2} \right )} + 8 x^{2} \log {\relax (2 )} + 8 x e^{3 x + 45} - x + \left (24 x^{2} + 2 \log {\left (3 x^{2} \right )} + 2 \log {\relax (2 )}\right ) e^{2 x + 30} + \left (32 x^{3} + 8 x \log {\left (3 x^{2} \right )} + 8 x \log {\relax (2 )}\right ) e^{x + 15} + e^{4 x + 60} + \log {\left (3 x^{2} \right )}^{2} + 2 \log {\relax (2 )} \log {\left (3 x^{2} \right )} + \log {\relax (2 )}^{2} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*exp(x+15)**2+(8*x**2+8*x)*exp(x+15)+16*x**2+4)*ln(3*x**2)+4*x*exp(x+15)**4+(24*x**2+8*x)*exp(x
+15)**3+(4*x*ln(2)+48*x**3+48*x**2+4)*exp(x+15)**2+((8*x**2+8*x)*ln(2)+32*x**4+96*x**3+16*x)*exp(x+15)+(16*x**
2+4)*ln(2)+64*x**4+16*x**2-x)/(x*ln(3*x**2)**2+(2*x*exp(x+15)**2+8*x**2*exp(x+15)+2*x*ln(2)+8*x**3)*ln(3*x**2)
+x*exp(x+15)**4+8*x**2*exp(x+15)**3+(2*x*ln(2)+24*x**3)*exp(x+15)**2+(8*x**2*ln(2)+32*x**4)*exp(x+15)+x*ln(2)*
*2+8*x**3*ln(2)+16*x**5-x**2),x)

[Out]

log(16*x**4 + 8*x**2*log(3*x**2) + 8*x**2*log(2) + 8*x*exp(3*x + 45) - x + (24*x**2 + 2*log(3*x**2) + 2*log(2)
)*exp(2*x + 30) + (32*x**3 + 8*x*log(3*x**2) + 8*x*log(2))*exp(x + 15) + exp(4*x + 60) + log(3*x**2)**2 + 2*lo
g(2)*log(3*x**2) + log(2)**2)

________________________________________________________________________________________