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3.31.61 \(\int \frac {196+168 x+400 x^2+268 x^3+329 x^4+152 x^5+120 x^6+32 x^7+16 x^8+(336 x+256 x^2+584 x^3+296 x^4+336 x^5+96 x^6+64 x^7) \log (x)+(256 x^2+144 x^3+312 x^4+96 x^5+96 x^6) \log ^2(x)+(96 x^3+32 x^4+64 x^5) \log ^3(x)+16 x^4 \log ^4(x)+e^{\frac {5}{14+6 x+13 x^2+4 x^3+4 x^4+(12 x+4 x^2+8 x^3) \log (x)+4 x^2 \log ^2(x)}} (-90-150 x-100 x^2-80 x^3+(-60-80 x-120 x^2) \log (x)-40 x \log ^2(x))}{196+168 x+400 x^2+268 x^3+329 x^4+152 x^5+120 x^6+32 x^7+16 x^8+(336 x+256 x^2+584 x^3+296 x^4+336 x^5+96 x^6+64 x^7) \log (x)+(256 x^2+144 x^3+312 x^4+96 x^5+96 x^6) \log ^2(x)+(96 x^3+32 x^4+64 x^5) \log ^3(x)+16 x^4 \log ^4(x)} \, dx\)

Optimal. Leaf size=25 \[ e^{\frac {5}{5+(3-x+2 x (1+x+\log (x)))^2}}+x \]

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Rubi [F]  time = 70.70, 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 {196+168 x+400 x^2+268 x^3+329 x^4+152 x^5+120 x^6+32 x^7+16 x^8+\left (336 x+256 x^2+584 x^3+296 x^4+336 x^5+96 x^6+64 x^7\right ) \log (x)+\left (256 x^2+144 x^3+312 x^4+96 x^5+96 x^6\right ) \log ^2(x)+\left (96 x^3+32 x^4+64 x^5\right ) \log ^3(x)+16 x^4 \log ^4(x)+\exp \left (\frac {5}{14+6 x+13 x^2+4 x^3+4 x^4+\left (12 x+4 x^2+8 x^3\right ) \log (x)+4 x^2 \log ^2(x)}\right ) \left (-90-150 x-100 x^2-80 x^3+\left (-60-80 x-120 x^2\right ) \log (x)-40 x \log ^2(x)\right )}{196+168 x+400 x^2+268 x^3+329 x^4+152 x^5+120 x^6+32 x^7+16 x^8+\left (336 x+256 x^2+584 x^3+296 x^4+336 x^5+96 x^6+64 x^7\right ) \log (x)+\left (256 x^2+144 x^3+312 x^4+96 x^5+96 x^6\right ) \log ^2(x)+\left (96 x^3+32 x^4+64 x^5\right ) \log ^3(x)+16 x^4 \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(196 + 168*x + 400*x^2 + 268*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^8 + (336*x + 256*x^2 + 584*
x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7)*Log[x] + (256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6)*Log[x]^2 +
 (96*x^3 + 32*x^4 + 64*x^5)*Log[x]^3 + 16*x^4*Log[x]^4 + E^(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + (12*x + 4*x
^2 + 8*x^3)*Log[x] + 4*x^2*Log[x]^2))*(-90 - 150*x - 100*x^2 - 80*x^3 + (-60 - 80*x - 120*x^2)*Log[x] - 40*x*L
og[x]^2))/(196 + 168*x + 400*x^2 + 268*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^8 + (336*x + 256*x^2
+ 584*x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7)*Log[x] + (256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6)*Log[
x]^2 + (96*x^3 + 32*x^4 + 64*x^5)*Log[x]^3 + 16*x^4*Log[x]^4),x]

[Out]

x - 30*Defer[Int][E^(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))/(14
+ 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 12*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] + 140*Defer
[Int][E^(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))/(x*(14 + 6*x + 1
3*x^2 + 4*x^3 + 4*x^4 + 12*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2), x] - 20*Defer[Int][(E^
(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*x)/(14 + 6*x + 13*x^2 +
4*x^3 + 4*x^4 + 12*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] - 60*Defer[Int][(E^(5/(14 +
6*x + 13*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*x^2)/(14 + 6*x + 13*x^2 + 4*x^3 +
 4*x^4 + 12*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] - 40*Defer[Int][(E^(5/(14 + 6*x + 1
3*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*x^3)/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4
+ 12*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] + 60*Defer[Int][(E^(5/(14 + 6*x + 13*x^2 +
 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*Log[x])/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 12
*x*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] - 40*Defer[Int][(E^(5/(14 + 6*x + 13*x^2 + 4*x
^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*x*Log[x])/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 12*x
*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] - 40*Defer[Int][(E^(5/(14 + 6*x + 13*x^2 + 4*x^3
 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))*x^2*Log[x])/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 12*x
*Log[x] + 4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)^2, x] - 10*Defer[Int][E^(5/(14 + 6*x + 13*x^2 + 4*x^3
+ 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2))/(x*(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 12*x*Log[x] +
4*x^2*Log[x] + 8*x^3*Log[x] + 4*x^2*Log[x]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {196+168 x+400 x^2+268 x^3+329 x^4+152 x^5+120 x^6+32 x^7+16 x^8+\left (336 x+256 x^2+584 x^3+296 x^4+336 x^5+96 x^6+64 x^7\right ) \log (x)+\left (256 x^2+144 x^3+312 x^4+96 x^5+96 x^6\right ) \log ^2(x)+\left (96 x^3+32 x^4+64 x^5\right ) \log ^3(x)+16 x^4 \log ^4(x)+\exp \left (\frac {5}{14+6 x+13 x^2+4 x^3+4 x^4+\left (12 x+4 x^2+8 x^3\right ) \log (x)+4 x^2 \log ^2(x)}\right ) \left (-90-150 x-100 x^2-80 x^3+\left (-60-80 x-120 x^2\right ) \log (x)-40 x \log ^2(x)\right )}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2} \, dx\\ &=\int \left (\frac {196}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {168 x}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {400 x^2}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {268 x^3}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {329 x^4}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {152 x^5}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {120 x^6}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {32 x^7}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {16 x^8}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {8 x \left (3+x+2 x^2\right ) \left (14+6 x+13 x^2+4 x^3+4 x^4\right ) \log (x)}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {8 x^2 \left (32+18 x+39 x^2+12 x^3+12 x^4\right ) \log ^2(x)}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {32 x^3 \left (3+x+2 x^2\right ) \log ^3(x)}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}+\frac {16 x^4 \log ^4(x)}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}-\frac {10 e^{\frac {5}{14+6 x+13 x^2+4 x^3+4 x^4+4 x \left (3+x+2 x^2\right ) \log (x)+4 x^2 \log ^2(x)}} (3+4 x+2 \log (x)) \left (3+x+2 x^2+2 x \log (x)\right )}{\left (14+6 x+13 x^2+4 x^3+4 x^4+12 x \log (x)+4 x^2 \log (x)+8 x^3 \log (x)+4 x^2 \log ^2(x)\right )^2}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.38, size = 50, normalized size = 2.00 \begin {gather*} e^{\frac {5}{14+6 x+13 x^2+4 x^3+4 x^4+4 x \left (3+x+2 x^2\right ) \log (x)+4 x^2 \log ^2(x)}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(196 + 168*x + 400*x^2 + 268*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^8 + (336*x + 256*x^2
+ 584*x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7)*Log[x] + (256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6)*Log[
x]^2 + (96*x^3 + 32*x^4 + 64*x^5)*Log[x]^3 + 16*x^4*Log[x]^4 + E^(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + (12*x
 + 4*x^2 + 8*x^3)*Log[x] + 4*x^2*Log[x]^2))*(-90 - 150*x - 100*x^2 - 80*x^3 + (-60 - 80*x - 120*x^2)*Log[x] -
40*x*Log[x]^2))/(196 + 168*x + 400*x^2 + 268*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^8 + (336*x + 25
6*x^2 + 584*x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7)*Log[x] + (256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6
)*Log[x]^2 + (96*x^3 + 32*x^4 + 64*x^5)*Log[x]^3 + 16*x^4*Log[x]^4),x]

[Out]

E^(5/(14 + 6*x + 13*x^2 + 4*x^3 + 4*x^4 + 4*x*(3 + x + 2*x^2)*Log[x] + 4*x^2*Log[x]^2)) + x

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fricas [B]  time = 0.57, size = 52, normalized size = 2.08 \begin {gather*} x + e^{\left (\frac {5}{4 \, x^{4} + 4 \, x^{2} \log \relax (x)^{2} + 4 \, x^{3} + 13 \, x^{2} + 4 \, {\left (2 \, x^{3} + x^{2} + 3 \, x\right )} \log \relax (x) + 6 \, x + 14}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-40*x*log(x)^2+(-120*x^2-80*x-60)*log(x)-80*x^3-100*x^2-150*x-90)*exp(5/(4*x^2*log(x)^2+(8*x^3+4*x
^2+12*x)*log(x)+4*x^4+4*x^3+13*x^2+6*x+14))+16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5+312
*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+120*
x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196)/(16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5
+312*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+
120*x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196),x, algorithm="fricas")

[Out]

x + e^(5/(4*x^4 + 4*x^2*log(x)^2 + 4*x^3 + 13*x^2 + 4*(2*x^3 + x^2 + 3*x)*log(x) + 6*x + 14))

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giac [B]  time = 1.55, size = 55, normalized size = 2.20 \begin {gather*} x + e^{\left (\frac {5}{4 \, x^{4} + 8 \, x^{3} \log \relax (x) + 4 \, x^{2} \log \relax (x)^{2} + 4 \, x^{3} + 4 \, x^{2} \log \relax (x) + 13 \, x^{2} + 12 \, x \log \relax (x) + 6 \, x + 14}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-40*x*log(x)^2+(-120*x^2-80*x-60)*log(x)-80*x^3-100*x^2-150*x-90)*exp(5/(4*x^2*log(x)^2+(8*x^3+4*x
^2+12*x)*log(x)+4*x^4+4*x^3+13*x^2+6*x+14))+16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5+312
*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+120*
x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196)/(16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5
+312*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+
120*x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196),x, algorithm="giac")

[Out]

x + e^(5/(4*x^4 + 8*x^3*log(x) + 4*x^2*log(x)^2 + 4*x^3 + 4*x^2*log(x) + 13*x^2 + 12*x*log(x) + 6*x + 14))

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maple [B]  time = 0.07, size = 56, normalized size = 2.24

method result size
risch \(x +{\mathrm e}^{\frac {5}{4 x^{2} \ln \relax (x )^{2}+8 x^{3} \ln \relax (x )+4 x^{4}+4 x^{2} \ln \relax (x )+4 x^{3}+12 x \ln \relax (x )+13 x^{2}+6 x +14}}\) \(56\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-40*x*ln(x)^2+(-120*x^2-80*x-60)*ln(x)-80*x^3-100*x^2-150*x-90)*exp(5/(4*x^2*ln(x)^2+(8*x^3+4*x^2+12*x)*
ln(x)+4*x^4+4*x^3+13*x^2+6*x+14))+16*x^4*ln(x)^4+(64*x^5+32*x^4+96*x^3)*ln(x)^3+(96*x^6+96*x^5+312*x^4+144*x^3
+256*x^2)*ln(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*ln(x)+16*x^8+32*x^7+120*x^6+152*x^5+32
9*x^4+268*x^3+400*x^2+168*x+196)/(16*x^4*ln(x)^4+(64*x^5+32*x^4+96*x^3)*ln(x)^3+(96*x^6+96*x^5+312*x^4+144*x^3
+256*x^2)*ln(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*ln(x)+16*x^8+32*x^7+120*x^6+152*x^5+32
9*x^4+268*x^3+400*x^2+168*x+196),x,method=_RETURNVERBOSE)

[Out]

x+exp(5/(4*x^2*ln(x)^2+8*x^3*ln(x)+4*x^4+4*x^2*ln(x)+4*x^3+12*x*ln(x)+13*x^2+6*x+14))

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maxima [B]  time = 0.55, size = 52, normalized size = 2.08 \begin {gather*} x + e^{\left (\frac {5}{4 \, x^{4} + 4 \, x^{2} \log \relax (x)^{2} + 4 \, x^{3} + 13 \, x^{2} + 4 \, {\left (2 \, x^{3} + x^{2} + 3 \, x\right )} \log \relax (x) + 6 \, x + 14}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-40*x*log(x)^2+(-120*x^2-80*x-60)*log(x)-80*x^3-100*x^2-150*x-90)*exp(5/(4*x^2*log(x)^2+(8*x^3+4*x
^2+12*x)*log(x)+4*x^4+4*x^3+13*x^2+6*x+14))+16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5+312
*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+120*
x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196)/(16*x^4*log(x)^4+(64*x^5+32*x^4+96*x^3)*log(x)^3+(96*x^6+96*x^5
+312*x^4+144*x^3+256*x^2)*log(x)^2+(64*x^7+96*x^6+336*x^5+296*x^4+584*x^3+256*x^2+336*x)*log(x)+16*x^8+32*x^7+
120*x^6+152*x^5+329*x^4+268*x^3+400*x^2+168*x+196),x, algorithm="maxima")

[Out]

x + e^(5/(4*x^4 + 4*x^2*log(x)^2 + 4*x^3 + 13*x^2 + 4*(2*x^3 + x^2 + 3*x)*log(x) + 6*x + 14))

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mupad [B]  time = 2.47, size = 55, normalized size = 2.20 \begin {gather*} x+{\mathrm {e}}^{\frac {5}{4\,x^4+8\,x^3\,\ln \relax (x)+4\,x^3+4\,x^2\,{\ln \relax (x)}^2+4\,x^2\,\ln \relax (x)+13\,x^2+12\,x\,\ln \relax (x)+6\,x+14}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((168*x + log(x)^2*(256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6) - exp(5/(6*x + 4*x^2*log(x)^2 + 13*x^2 +
 4*x^3 + 4*x^4 + log(x)*(12*x + 4*x^2 + 8*x^3) + 14))*(150*x + 40*x*log(x)^2 + log(x)*(80*x + 120*x^2 + 60) +
100*x^2 + 80*x^3 + 90) + 16*x^4*log(x)^4 + log(x)^3*(96*x^3 + 32*x^4 + 64*x^5) + log(x)*(336*x + 256*x^2 + 584
*x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7) + 400*x^2 + 268*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^
8 + 196)/(168*x + log(x)^2*(256*x^2 + 144*x^3 + 312*x^4 + 96*x^5 + 96*x^6) + 16*x^4*log(x)^4 + log(x)^3*(96*x^
3 + 32*x^4 + 64*x^5) + log(x)*(336*x + 256*x^2 + 584*x^3 + 296*x^4 + 336*x^5 + 96*x^6 + 64*x^7) + 400*x^2 + 26
8*x^3 + 329*x^4 + 152*x^5 + 120*x^6 + 32*x^7 + 16*x^8 + 196),x)

[Out]

x + exp(5/(6*x + 4*x^2*log(x) + 8*x^3*log(x) + 4*x^2*log(x)^2 + 12*x*log(x) + 13*x^2 + 4*x^3 + 4*x^4 + 14))

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sympy [B]  time = 1.26, size = 51, normalized size = 2.04 \begin {gather*} x + e^{\frac {5}{4 x^{4} + 4 x^{3} + 4 x^{2} \log {\relax (x )}^{2} + 13 x^{2} + 6 x + \left (8 x^{3} + 4 x^{2} + 12 x\right ) \log {\relax (x )} + 14}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-40*x*ln(x)**2+(-120*x**2-80*x-60)*ln(x)-80*x**3-100*x**2-150*x-90)*exp(5/(4*x**2*ln(x)**2+(8*x**3
+4*x**2+12*x)*ln(x)+4*x**4+4*x**3+13*x**2+6*x+14))+16*x**4*ln(x)**4+(64*x**5+32*x**4+96*x**3)*ln(x)**3+(96*x**
6+96*x**5+312*x**4+144*x**3+256*x**2)*ln(x)**2+(64*x**7+96*x**6+336*x**5+296*x**4+584*x**3+256*x**2+336*x)*ln(
x)+16*x**8+32*x**7+120*x**6+152*x**5+329*x**4+268*x**3+400*x**2+168*x+196)/(16*x**4*ln(x)**4+(64*x**5+32*x**4+
96*x**3)*ln(x)**3+(96*x**6+96*x**5+312*x**4+144*x**3+256*x**2)*ln(x)**2+(64*x**7+96*x**6+336*x**5+296*x**4+584
*x**3+256*x**2+336*x)*ln(x)+16*x**8+32*x**7+120*x**6+152*x**5+329*x**4+268*x**3+400*x**2+168*x+196),x)

[Out]

x + exp(5/(4*x**4 + 4*x**3 + 4*x**2*log(x)**2 + 13*x**2 + 6*x + (8*x**3 + 4*x**2 + 12*x)*log(x) + 14))

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