3.67.74 \(\int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x (49-16 x+x^2)+(280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)) \log (x)+(15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)) \log ^2(x)+(100 e^x+100 e^{2 x}) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+(140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)) \log (x)+(170+300 e^x+140 e^{2 x}+10 x) \log ^2(x)+(100+100 e^x) \log ^3(x)+25 \log ^4(x)} \, dx\)

Optimal. Leaf size=30 \[ e^x-\frac {3 x}{-2+e^{2 x}-x-5 \left (1+e^x+\log (x)\right )^2} \]

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Rubi [F]  time = 4.08, 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 {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-9 + 80*E^(4*x) + 16*E^(5*x) + E^(2*x)*(152 - 4*x) + E^(3*x)*(156 + 8*x) + E^x*(49 - 16*x + x^2) + (280*E
^(3*x) + 80*E^(4*x) + E^x*(170 - 10*x) + E^(2*x)*(340 + 20*x))*Log[x] + (15 + 300*E^(2*x) + 140*E^(3*x) + E^x*
(170 + 10*x))*Log[x]^2 + (100*E^x + 100*E^(2*x))*Log[x]^3 + 25*E^x*Log[x]^4)/(49 + 80*E^(3*x) + 16*E^(4*x) + 1
4*x + x^2 + E^(2*x)*(156 + 8*x) + E^x*(140 + 20*x) + (140 + 280*E^(2*x) + 80*E^(3*x) + 20*x + E^x*(340 + 20*x)
)*Log[x] + (170 + 300*E^x + 140*E^(2*x) + 10*x)*Log[x]^2 + (100 + 100*E^x)*Log[x]^3 + 25*Log[x]^4),x]

[Out]

E^x - 30*Defer[Int][(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^(-2), x] - 30*Defer[
Int][E^x/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^2, x] + 39*Defer[Int][x/(7 + 10
*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^2, x] + 30*Defer[Int][(E^x*x)/(7 + 10*E^x + 4*E
^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^2, x] + 6*Defer[Int][x^2/(7 + 10*E^x + 4*E^(2*x) + x + 10
*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^2, x] - 30*Defer[Int][Log[x]/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 1
0*E^x*Log[x] + 5*Log[x]^2)^2, x] + 60*Defer[Int][(x*Log[x])/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*L
og[x] + 5*Log[x]^2)^2, x] + 30*Defer[Int][(E^x*x*Log[x])/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[
x] + 5*Log[x]^2)^2, x] + 30*Defer[Int][(x*Log[x]^2)/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] +
5*Log[x]^2)^2, x] + 3*Defer[Int][(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)^(-1), x
] - 6*Defer[Int][x/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9+80 e^{4 x}+16 e^{5 x}-4 e^{2 x} (-38+x)+4 e^{3 x} (39+2 x)+e^x \left (49-16 x+x^2\right )+10 e^x \left (17+28 e^{2 x}+8 e^{3 x}-x+2 e^x (17+x)\right ) \log (x)+5 \left (3+60 e^{2 x}+28 e^{3 x}+2 e^x (17+x)\right ) \log ^2(x)+100 e^x \left (1+e^x\right ) \log ^3(x)+25 e^x \log ^4(x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \left (1+e^x\right ) \log (x)+5 \log ^2(x)\right )^2} \, dx\\ &=\int \left (e^x-\frac {3 (-1+2 x)}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)}+\frac {3 \left (-10-10 e^x+13 x+10 e^x x+2 x^2-10 \log (x)+20 x \log (x)+10 e^x x \log (x)+10 x \log ^2(x)\right )}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}\right ) \, dx\\ &=-\left (3 \int \frac {-1+2 x}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)} \, dx\right )+3 \int \frac {-10-10 e^x+13 x+10 e^x x+2 x^2-10 \log (x)+20 x \log (x)+10 e^x x \log (x)+10 x \log ^2(x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+\int e^x \, dx\\ &=e^x+3 \int \left (-\frac {10}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}-\frac {10 e^x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {13 x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {10 e^x x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {2 x^2}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}-\frac {10 \log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {20 x \log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {10 e^x x \log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}+\frac {10 x \log ^2(x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2}\right ) \, dx-3 \int \left (-\frac {1}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)}+\frac {2 x}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)}\right ) \, dx\\ &=e^x+3 \int \frac {1}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)} \, dx+6 \int \frac {x^2}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx-6 \int \frac {x}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)} \, dx-30 \int \frac {1}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx-30 \int \frac {e^x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+30 \int \frac {e^x x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx-30 \int \frac {\log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+30 \int \frac {e^x x \log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+30 \int \frac {x \log ^2(x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+39 \int \frac {x}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx+60 \int \frac {x \log (x)}{\left (7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.17, size = 41, normalized size = 1.37 \begin {gather*} e^x+\frac {3 x}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-9 + 80*E^(4*x) + 16*E^(5*x) + E^(2*x)*(152 - 4*x) + E^(3*x)*(156 + 8*x) + E^x*(49 - 16*x + x^2) +
(280*E^(3*x) + 80*E^(4*x) + E^x*(170 - 10*x) + E^(2*x)*(340 + 20*x))*Log[x] + (15 + 300*E^(2*x) + 140*E^(3*x)
+ E^x*(170 + 10*x))*Log[x]^2 + (100*E^x + 100*E^(2*x))*Log[x]^3 + 25*E^x*Log[x]^4)/(49 + 80*E^(3*x) + 16*E^(4*
x) + 14*x + x^2 + E^(2*x)*(156 + 8*x) + E^x*(140 + 20*x) + (140 + 280*E^(2*x) + 80*E^(3*x) + 20*x + E^x*(340 +
20*x))*Log[x] + (170 + 300*E^x + 140*E^(2*x) + 10*x)*Log[x]^2 + (100 + 100*E^x)*Log[x]^3 + 25*Log[x]^4),x]

[Out]

E^x + (3*x)/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Log[x]^2)

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fricas [B]  time = 0.56, size = 71, normalized size = 2.37 \begin {gather*} \frac {5 \, e^{x} \log \relax (x)^{2} + {\left (x + 7\right )} e^{x} + 10 \, {\left (e^{\left (2 \, x\right )} + e^{x}\right )} \log \relax (x) + 3 \, x + 4 \, e^{\left (3 \, x\right )} + 10 \, e^{\left (2 \, x\right )}}{10 \, {\left (e^{x} + 1\right )} \log \relax (x) + 5 \, \log \relax (x)^{2} + x + 4 \, e^{\left (2 \, x\right )} + 10 \, e^{x} + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp(x)^3+300*exp(x)^2+(10*x+170)*exp(x)+
15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+
(8*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+(100*exp(x)+100)*log(x)^3+(140*exp
(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80*exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+8
0*exp(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="fricas")

[Out]

(5*e^x*log(x)^2 + (x + 7)*e^x + 10*(e^(2*x) + e^x)*log(x) + 3*x + 4*e^(3*x) + 10*e^(2*x))/(10*(e^x + 1)*log(x)
+ 5*log(x)^2 + x + 4*e^(2*x) + 10*e^x + 7)

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giac [B]  time = 5.98, size = 5359, normalized size = 178.63 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp(x)^3+300*exp(x)^2+(10*x+170)*exp(x)+
15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+
(8*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+(100*exp(x)+100)*log(x)^3+(140*exp
(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80*exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+8
0*exp(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="giac")

[Out]

(2500*x^5*e^(3*x)*log(x)^6 - 1000*x^6*e^(3*x)*log(x)^4 + 3000*x^6*e^(2*x)*log(x)^4 + 5000*x^5*e^(4*x)*log(x)^5
+ 15000*x^5*e^(3*x)*log(x)^5 + 750*x^5*e^x*log(x)^5 - 2000*x^4*e^(5*x)*log(x)^6 + 4500*x^4*e^(3*x)*log(x)^6 +
5000*x^4*e^(2*x)*log(x)^6 + 125*x^4*e^x*log(x)^6 - 700*x^7*e^(3*x)*log(x)^2 - 1800*x^7*e^(2*x)*log(x)^2 - 300
0*x^6*e^(4*x)*log(x)^3 - 4000*x^6*e^(3*x)*log(x)^3 + 12000*x^6*e^(2*x)*log(x)^3 - 450*x^6*e^x*log(x)^3 + 2800*
x^5*e^(5*x)*log(x)^4 + 22600*x^5*e^(4*x)*log(x)^4 + 33200*x^5*e^(3*x)*log(x)^4 + 7300*x^5*e^(2*x)*log(x)^4 + 8
200*x^5*e^x*log(x)^4 - 4000*x^4*e^(6*x)*log(x)^5 - 12000*x^4*e^(5*x)*log(x)^5 + 9000*x^4*e^(4*x)*log(x)^5 + 29
000*x^4*e^(3*x)*log(x)^5 + 24250*x^4*e^(2*x)*log(x)^5 - 5000*x^3*e^(4*x)*log(x)^6 + 10000*x^3*e^(2*x)*log(x)^6
+ 2500*x^3*e^x*log(x)^6 - 80*x^8*e^(3*x) - 480*x^8*e^(2*x) - 800*x^7*e^(4*x)*log(x) - 1400*x^7*e^(3*x)*log(x)
- 3600*x^7*e^(2*x)*log(x) - 120*x^7*e^x*log(x) - 640*x^6*e^(5*x)*log(x)^2 - 7560*x^6*e^(4*x)*log(x)^2 - 9760*
x^6*e^(3*x)*log(x)^2 + 8920*x^6*e^(2*x)*log(x)^2 - 4085*x^6*e^x*log(x)^2 + 2400*x^5*e^(6*x)*log(x)^3 + 11200*x
^5*e^(5*x)*log(x)^3 + 28000*x^5*e^(4*x)*log(x)^3 + 34600*x^5*e^(3*x)*log(x)^3 + 17650*x^5*e^(2*x)*log(x)^3 + 2
4700*x^5*e^x*log(x)^3 + 75*x^5*log(x)^4 - 1600*x^4*e^(7*x)*log(x)^4 - 20000*x^4*e^(6*x)*log(x)^4 - 24400*x^4*e
^(5*x)*log(x)^4 + 35000*x^4*e^(4*x)*log(x)^4 + 61100*x^4*e^(3*x)*log(x)^4 + 42050*x^4*e^(2*x)*log(x)^4 + 12750
*x^4*e^x*log(x)^4 - 6000*x^3*e^(5*x)*log(x)^5 - 30000*x^3*e^(4*x)*log(x)^5 + 11000*x^3*e^(3*x)*log(x)^5 + 5050
0*x^3*e^(2*x)*log(x)^5 + 7250*x^3*e^x*log(x)^5 - 2500*x^2*e^(3*x)*log(x)^6 + 5000*x^2*e^x*log(x)^6 - 256*x^7*e
^(5*x) - 416*x^7*e^(4*x) - 1244*x^7*e^(3*x) - 4168*x^7*e^(2*x) - 844*x^7*e^x + 640*x^6*e^(6*x)*log(x) - 1280*x
^6*e^(5*x)*log(x) - 9960*x^6*e^(4*x)*log(x) - 11840*x^6*e^(3*x)*log(x) + 760*x^6*e^(2*x)*log(x) - 7060*x^6*e^x
*log(x) - 45*x^6*log(x)^2 + 960*x^5*e^(7*x)*log(x)^2 + 7200*x^5*e^(6*x)*log(x)^2 + 13840*x^5*e^(5*x)*log(x)^2
+ 10680*x^5*e^(4*x)*log(x)^2 + 11440*x^5*e^(3*x)*log(x)^2 - 3570*x^5*e^(2*x)*log(x)^2 + 20325*x^5*e^x*log(x)^2
+ 300*x^5*log(x)^3 - 6400*x^4*e^(7*x)*log(x)^3 - 34400*x^4*e^(6*x)*log(x)^3 - 20400*x^4*e^(5*x)*log(x)^3 + 49
400*x^4*e^(4*x)*log(x)^3 + 39900*x^4*e^(3*x)*log(x)^3 + 15150*x^4*e^(2*x)*log(x)^3 + 32350*x^4*e^x*log(x)^3 +
1725*x^4*log(x)^4 + 4000*x^3*e^(6*x)*log(x)^4 - 30000*x^3*e^(5*x)*log(x)^4 - 80000*x^3*e^(4*x)*log(x)^4 + 3450
0*x^3*e^(3*x)*log(x)^4 + 95000*x^3*e^(2*x)*log(x)^4 + 10750*x^3*e^x*log(x)^4 + 5000*x^2*e^(4*x)*log(x)^5 - 150
00*x^2*e^(3*x)*log(x)^5 - 10000*x^2*e^(2*x)*log(x)^5 + 25000*x^2*e^x*log(x)^5 - 12*x^7 + 256*x^6*e^(7*x) + 640
*x^6*e^(6*x) - 1856*x^6*e^(5*x) - 4344*x^6*e^(4*x) - 4556*x^6*e^(3*x) - 3376*x^6*e^(2*x) - 7005*x^6*e^x - 90*x
^6*log(x) + 1920*x^5*e^(7*x)*log(x) + 9120*x^5*e^(6*x)*log(x) + 9440*x^5*e^(5*x)*log(x) - 8160*x^5*e^(4*x)*log
(x) - 8740*x^5*e^(3*x)*log(x) - 4770*x^5*e^(2*x)*log(x) + 6530*x^5*e^x*log(x) - 585*x^5*log(x)^2 - 7360*x^4*e^
(7*x)*log(x)^2 - 27200*x^4*e^(6*x)*log(x)^2 - 3200*x^4*e^(5*x)*log(x)^2 + 56840*x^4*e^(4*x)*log(x)^2 - 13980*x
^4*e^(3*x)*log(x)^2 - 51510*x^4*e^(2*x)*log(x)^2 + 5360*x^4*e^x*log(x)^2 + 6300*x^4*log(x)^3 + 3200*x^3*e^(7*x
)*log(x)^3 + 16000*x^3*e^(6*x)*log(x)^3 - 58400*x^3*e^(5*x)*log(x)^3 - 123600*x^3*e^(4*x)*log(x)^3 + 53500*x^3
*e^(3*x)*log(x)^3 + 103800*x^3*e^(2*x)*log(x)^3 - 23425*x^3*e^x*log(x)^3 + 7500*x^3*log(x)^4 + 16000*x^2*e^(5*
x)*log(x)^4 + 25000*x^2*e^(4*x)*log(x)^4 - 66500*x^2*e^(3*x)*log(x)^4 - 50500*x^2*e^(2*x)*log(x)^4 + 60125*x^2
*e^x*log(x)^4 + 5000*x*e^(3*x)*log(x)^5 - 10000*x*e^x*log(x)^5 - 321*x^6 + 1728*x^5*e^(7*x) + 4960*x^5*e^(6*x)
+ 2080*x^5*e^(5*x) - 8632*x^5*e^(4*x) - 2376*x^5*e^(3*x) + 3734*x^5*e^(2*x) - 2718*x^5*e^x - 1590*x^5*log(x)
- 4480*x^4*e^(7*x)*log(x) - 9760*x^4*e^(6*x)*log(x) + 18960*x^4*e^(5*x)*log(x) + 44400*x^4*e^(4*x)*log(x) - 37
320*x^4*e^(3*x)*log(x) - 46610*x^4*e^(2*x)*log(x) + 6465*x^4*e^x*log(x) + 4095*x^4*log(x)^2 + 9600*x^3*e^(7*x)
*log(x)^2 + 16000*x^3*e^(6*x)*log(x)^2 - 64000*x^3*e^(5*x)*log(x)^2 - 89400*x^3*e^(4*x)*log(x)^2 + 106000*x^3*
e^(3*x)*log(x)^2 + 68650*x^3*e^(2*x)*log(x)^2 - 97575*x^3*e^x*log(x)^2 + 17775*x^3*log(x)^3 + 4000*x^2*e^(6*x)
*log(x)^3 + 64000*x^2*e^(5*x)*log(x)^3 + 37000*x^2*e^(4*x)*log(x)^3 - 154000*x^2*e^(3*x)*log(x)^3 - 68750*x^2*
e^(2*x)*log(x)^3 + 96250*x^2*e^x*log(x)^3 + 9000*x^2*log(x)^4 + 5000*x*e^(4*x)*log(x)^4 + 25000*x*e^(3*x)*log(
x)^4 - 10000*x*e^(2*x)*log(x)^4 - 47500*x*e^x*log(x)^4 - 2019*x^5 - 1344*x^4*e^(7*x) + 960*x^4*e^(6*x) + 13872
*x^4*e^(5*x) + 10552*x^4*e^(4*x) - 19784*x^4*e^(3*x) - 13050*x^4*e^(2*x) + 11367*x^4*e^x + 135*x^4*log(x) + 41
60*x^3*e^(7*x)*log(x) - 2400*x^3*e^(6*x)*log(x) - 34480*x^3*e^(5*x)*log(x) - 13920*x^3*e^(4*x)*log(x) + 90760*
x^3*e^(3*x)*log(x) + 20910*x^3*e^(2*x)*log(x) - 67755*x^3*e^x*log(x) + 4350*x^3*log(x)^2 - 1600*x^2*e^(7*x)*lo
g(x)^2 + 12000*x^2*e^(6*x)*log(x)^2 + 71600*x^2*e^(5*x)*log(x)^2 + 14600*x^2*e^(4*x)*log(x)^2 - 141900*x^2*e^(
3*x)*log(x)^2 - 17750*x^2*e^(2*x)*log(x)^2 + 99950*x^2*e^x*log(x)^2 + 7500*x^2*log(x)^3 - 6000*x*e^(5*x)*log(x
)^3 + 20000*x*e^(4*x)*log(x)^3 + 55500*x*e^(3*x)*log(x)^3 - 35000*x*e^(2*x)*log(x)^3 - 84500*x*e^x*log(x)^3 -
2500*e^(3*x)*log(x)^4 + 5000*e^x*log(x)^4 - 1698*x^4 - 640*x^3*e^(7*x) - 4960*x^3*e^(6*x) - 8960*x^3*e^(5*x) +
8920*x^3*e^(4*x) + 18720*x^3*e^(3*x) - 11100*x^3*e^(2*x) - 19555*x^3*e^x - 615*x^3*log(x) - 3200*x^2*e^(7*x)*
log(x) + 6400*x^2*e^(6*x)*log(x) + 22000*x^2*e^(5*x)*log(x) - 14600*x^2*e^(4*x)*log(x) - 59700*x^2*e^(3*x)*log
(x) + 31350*x^2*e^(2*x)*log(x) + 66650*x^2*e^x*log(x) - 19200*x^2*log(x)^2 - 4000*x*e^(6*x)*log(x)^2 - 18000*x
*e^(5*x)*log(x)^2 + 29000*x*e^(4*x)*log(x)^2 + 70500*x*e^(3*x)*log(x)^2 - 45000*x*e^(2*x)*log(x)^2 - 85500*x*e
^x*log(x)^2 - 9000*x*log(x)^3 - 5000*e^(4*x)*log(x)^3 - 10000*e^(3*x)*log(x)^3 + 10000*e^(2*x)*log(x)^3 + 2000
0*e^x*log(x)^3 + 1740*x^3 + 1600*x^2*e^(7*x) + 2400*x^2*e^(6*x) - 6480*x^2*e^(5*x) - 17000*x^2*e^(4*x) + 2820*
x^2*e^(3*x) + 20010*x^2*e^(2*x) + 4305*x^2*e^x - 12900*x^2*log(x) - 8000*x*e^(6*x)*log(x) - 4800*x*e^(5*x)*log
(x) + 23000*x*e^(4*x)*log(x) + 13700*x*e^(3*x)*log(x) - 34200*x*e^(2*x)*log(x) - 23700*x*e^x*log(x) - 6000*x*l
og(x)^2 - 2000*e^(5*x)*log(x)^2 - 15000*e^(4*x)*log(x)^2 - 7000*e^(3*x)*log(x)^2 + 30000*e^(2*x)*log(x)^2 + 22
000*e^x*log(x)^2 - 1920*x^2 + 4000*x*e^(6*x) + 9200*x*e^(5*x) - 3000*x*e^(4*x) - 20100*x*e^(3*x) - 4200*x*e^(2
*x) + 12400*x*e^x + 11400*x*log(x) - 4000*e^(5*x)*log(x) - 5000*e^(4*x)*log(x) + 6000*e^(3*x)*log(x) + 10000*e
^(2*x)*log(x) + 4000*e^x*log(x) + 2400*x + 2000*e^(5*x) + 5000*e^(4*x) - 500*e^(3*x) - 10000*e^(2*x) - 7000*e^
x)/(2500*x^5*e^(2*x)*log(x)^6 - 1000*x^6*e^(2*x)*log(x)^4 + 5000*x^5*e^(3*x)*log(x)^5 + 15000*x^5*e^(2*x)*log(
x)^5 - 2000*x^4*e^(4*x)*log(x)^6 + 4500*x^4*e^(2*x)*log(x)^6 + 5000*x^4*e^x*log(x)^6 - 700*x^7*e^(2*x)*log(x)^
2 - 3000*x^6*e^(3*x)*log(x)^3 - 4000*x^6*e^(2*x)*log(x)^3 + 2800*x^5*e^(4*x)*log(x)^4 + 25000*x^5*e^(3*x)*log(
x)^4 + 33200*x^5*e^(2*x)*log(x)^4 - 2000*x^5*e^x*log(x)^4 - 4000*x^4*e^(5*x)*log(x)^5 - 12000*x^4*e^(4*x)*log(
x)^5 + 9000*x^4*e^(3*x)*log(x)^5 + 32000*x^4*e^(2*x)*log(x)^5 + 30250*x^4*e^x*log(x)^5 + 125*x^4*log(x)^6 - 50
00*x^3*e^(3*x)*log(x)^6 + 10000*x^3*e^x*log(x)^6 - 80*x^8*e^(2*x) - 800*x^7*e^(3*x)*log(x) - 1400*x^7*e^(2*x)*
log(x) - 640*x^6*e^(4*x)*log(x)^2 - 9000*x^6*e^(3*x)*log(x)^2 - 9760*x^6*e^(2*x)*log(x)^2 - 1400*x^6*e^x*log(x
)^2 + 2400*x^5*e^(5*x)*log(x)^3 + 11200*x^5*e^(4*x)*log(x)^3 + 37600*x^5*e^(3*x)*log(x)^3 + 29800*x^5*e^(2*x)*
log(x)^3 - 8150*x^5*e^x*log(x)^3 - 50*x^5*log(x)^4 - 1600*x^4*e^(6*x)*log(x)^4 - 20000*x^4*e^(5*x)*log(x)^4 -
24400*x^4*e^(4*x)*log(x)^4 + 41000*x^4*e^(3*x)*log(x)^4 + 88100*x^4*e^(2*x)*log(x)^4 + 67250*x^4*e^x*log(x)^4
+ 750*x^4*log(x)^5 - 6000*x^3*e^(4*x)*log(x)^5 - 30000*x^3*e^(3*x)*log(x)^5 + 11000*x^3*e^(2*x)*log(x)^5 + 550
00*x^3*e^x*log(x)^5 + 2500*x^3*log(x)^6 - 2500*x^2*e^(2*x)*log(x)^6 - 256*x^7*e^(4*x) - 800*x^7*e^(3*x) - 1244
*x^7*e^(2*x) - 160*x^7*e^x + 640*x^6*e^(5*x)*log(x) - 1280*x^6*e^(4*x)*log(x) - 12840*x^6*e^(3*x)*log(x) - 123
20*x^6*e^(2*x)*log(x) - 2840*x^6*e^x*log(x) - 35*x^6*log(x)^2 + 960*x^5*e^(6*x)*log(x)^2 + 7200*x^5*e^(5*x)*lo
g(x)^2 + 13840*x^5*e^(4*x)*log(x)^2 + 19800*x^5*e^(3*x)*log(x)^2 - 4160*x^5*e^(2*x)*log(x)^2 - 20250*x^5*e^x*l
og(x)^2 - 200*x^5*log(x)^3 - 6400*x^4*e^(6*x)*log(x)^3 - 34400*x^4*e^(5*x)*log(x)^3 - 18000*x^4*e^(4*x)*log(x)
^3 + 61400*x^4*e^(3*x)*log(x)^3 + 108300*x^4*e^(2*x)*log(x)^3 + 69150*x^4*e^x*log(x)^3 + 750*x^4*log(x)^4 + 40
00*x^3*e^(5*x)*log(x)^4 - 30000*x^3*e^(4*x)*log(x)^4 - 80000*x^3*e^(3*x)*log(x)^4 + 40500*x^3*e^(2*x)*log(x)^4
+ 114500*x^3*e^x*log(x)^4 + 14750*x^3*log(x)^5 + 5000*x^2*e^(3*x)*log(x)^5 - 15000*x^2*e^(2*x)*log(x)^5 - 100
00*x^2*e^x*log(x)^5 + 5000*x^2*log(x)^6 - 4*x^7 + 256*x^6*e^(6*x) + 640*x^6*e^(5*x) - 1856*x^6*e^(4*x) - 7320*
x^6*e^(3*x) - 6956*x^6*e^(2*x) - 2560*x^6*e^x - 70*x^6*log(x) + 1920*x^5*e^(6*x)*log(x) + 9120*x^5*e^(5*x)*log
(x) + 9440*x^5*e^(4*x)*log(x) - 4320*x^5*e^(3*x)*log(x) - 28180*x^5*e^(2*x)*log(x) - 23370*x^5*e^x*log(x) - 11
25*x^5*log(x)^2 - 7360*x^4*e^(6*x)*log(x)^2 - 27200*x^4*e^(5*x)*log(x)^2 - 800*x^4*e^(4*x)*log(x)^2 + 54200*x^
4*e^(3*x)*log(x)^2 + 58020*x^4*e^(2*x)*log(x)^2 + 17250*x^4*e^x*log(x)^2 - 1850*x^4*log(x)^3 + 3200*x^3*e^(6*x
)*log(x)^3 + 16000*x^3*e^(5*x)*log(x)^3 - 58400*x^3*e^(4*x)*log(x)^3 - 126000*x^3*e^(3*x)*log(x)^3 + 35500*x^3
*e^(2*x)*log(x)^3 + 120000*x^3*e^x*log(x)^3 + 31750*x^3*log(x)^4 + 16000*x^2*e^(4*x)*log(x)^4 + 25000*x^2*e^(3
*x)*log(x)^4 - 66500*x^2*e^(2*x)*log(x)^4 - 55000*x^2*e^x*log(x)^4 + 25000*x^2*log(x)^5 + 5000*x*e^(2*x)*log(x
)^5 - 135*x^6 + 1728*x^5*e^(6*x) + 4960*x^5*e^(5*x) + 2080*x^5*e^(4*x) - 8920*x^5*e^(3*x) - 17256*x^5*e^(2*x)
- 12190*x^5*e^x - 1810*x^5*log(x) - 4480*x^4*e^(6*x)*log(x) - 9760*x^4*e^(5*x)*log(x) + 17520*x^4*e^(4*x)*log(
x) + 40560*x^4*e^(3*x)*log(x) + 6840*x^4*e^(2*x)*log(x) - 19490*x^4*e^x*log(x) - 8440*x^4*log(x)^2 + 9600*x^3*
e^(6*x)*log(x)^2 + 16000*x^3*e^(5*x)*log(x)^2 - 66400*x^3*e^(4*x)*log(x)^2 - 99000*x^3*e^(3*x)*log(x)^2 + 2920
0*x^3*e^(2*x)*log(x)^2 + 68650*x^3*e^x*log(x)^2 + 32825*x^3*log(x)^3 + 4000*x^2*e^(5*x)*log(x)^3 + 64000*x^2*e
^(4*x)*log(x)^3 + 37000*x^2*e^(3*x)*log(x)^3 - 163000*x^2*e^(2*x)*log(x)^3 - 107750*x^2*e^x*log(x)^3 + 45125*x
^2*log(x)^4 + 5000*x*e^(3*x)*log(x)^4 + 25000*x*e^(2*x)*log(x)^4 - 10000*x*e^x*log(x)^4 - 10000*x*log(x)^5 - 1
428*x^5 - 1344*x^4*e^(6*x) + 960*x^4*e^(5*x) + 12432*x^4*e^(4*x) + 11800*x^4*e^(3*x) - 8264*x^4*e^(2*x) - 1395
0*x^4*e^x - 10365*x^4*log(x) + 4160*x^3*e^(6*x)*log(x) - 2400*x^3*e^(5*x)*log(x) - 34480*x^3*e^(4*x)*log(x) -
16800*x^3*e^(3*x)*log(x) + 50560*x^3*e^(2*x)*log(x) + 33450*x^3*e^x*log(x) + 10575*x^3*log(x)^2 - 1600*x^2*e^(
6*x)*log(x)^2 + 12000*x^2*e^(5*x)*log(x)^2 + 71600*x^2*e^(4*x)*log(x)^2 + 11000*x^2*e^(3*x)*log(x)^2 - 144900*
x^2*e^(2*x)*log(x)^2 - 76250*x^2*e^x*log(x)^2 + 43000*x^2*log(x)^3 - 6000*x*e^(4*x)*log(x)^3 + 20000*x*e^(3*x)
*log(x)^3 + 55500*x*e^(2*x)*log(x)^3 - 35000*x*e^x*log(x)^3 - 47500*x*log(x)^4 - 2500*e^(2*x)*log(x)^4 - 5403*
x^4 - 640*x^3*e^(6*x) - 4960*x^3*e^(5*x) - 7520*x^3*e^(4*x) + 6040*x^3*e^(3*x) + 19680*x^3*e^(2*x) + 7860*x^3*
e^x - 4005*x^3*log(x) - 3200*x^2*e^(6*x)*log(x) + 6400*x^2*e^(5*x)*log(x) + 22000*x^2*e^(4*x)*log(x) - 9800*x^
2*e^(3*x)*log(x) - 36900*x^2*e^(2*x)*log(x) + 5250*x^2*e^x*log(x) + 26450*x^2*log(x)^2 - 4000*x*e^(5*x)*log(x)
^2 - 18000*x*e^(4*x)*log(x)^2 + 29000*x*e^(3*x)*log(x)^2 + 70500*x*e^(2*x)*log(x)^2 - 27000*x*e^x*log(x)^2 - 7
7000*x*log(x)^3 - 5000*e^(3*x)*log(x)^3 - 10000*e^(2*x)*log(x)^3 + 10000*e^x*log(x)^3 + 5000*log(x)^4 - 3535*x
^3 + 1600*x^2*e^(6*x) + 2400*x^2*e^(5*x) - 6480*x^2*e^(4*x) - 15800*x^2*e^(3*x) - 7380*x^2*e^(2*x) + 6750*x^2*
e^x + 19400*x^2*log(x) - 8000*x*e^(5*x)*log(x) - 4800*x*e^(4*x)*log(x) + 23000*x*e^(3*x)*log(x) + 19700*x*e^(2
*x)*log(x) - 9000*x*e^x*log(x) - 54000*x*log(x)^2 - 2000*e^(4*x)*log(x)^2 - 15000*e^(3*x)*log(x)^2 - 7000*e^(2
*x)*log(x)^2 + 30000*e^x*log(x)^2 + 20000*log(x)^3 + 7005*x^2 + 4000*x*e^(5*x) + 9200*x*e^(4*x) - 3000*x*e^(3*
x) - 21300*x*e^(2*x) - 15000*x*e^x - 10200*x*log(x) - 4000*e^(4*x)*log(x) - 5000*e^(3*x)*log(x) + 6000*e^(2*x)
*log(x) + 10000*e^x*log(x) + 22000*log(x)^2 - 1700*x + 2000*e^(4*x) + 5000*e^(3*x) - 500*e^(2*x) - 10000*e^x +
4000*log(x) - 7000)

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maple [A]  time = 0.05, size = 38, normalized size = 1.27

method	result	size
risch	\({\mathrm e}^{x}+\frac {3 x}{5 \ln \relax (x )^{2}+10 \,{\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e}^{2 x}+10 \ln \relax (x )+10 \,{\mathrm e}^{x}+x +7}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((25*exp(x)*ln(x)^4+(100*exp(x)^2+100*exp(x))*ln(x)^3+(140*exp(x)^3+300*exp(x)^2+(10*x+170)*exp(x)+15)*ln(x
)^2+(80*exp(x)^4+280*exp(x)^3+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*ln(x)+16*exp(x)^5+80*exp(x)^4+(8*x+156)*
exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*ln(x)^4+(100*exp(x)+100)*ln(x)^3+(140*exp(x)^2+300*ex
p(x)+10*x+170)*ln(x)^2+(80*exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*ln(x)+16*exp(x)^4+80*exp(x)^3+(8*
x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x,method=_RETURNVERBOSE)

[Out]

exp(x)+3*x/(5*ln(x)^2+10*exp(x)*ln(x)+4*exp(2*x)+10*ln(x)+10*exp(x)+x+7)

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maxima [B]  time = 0.57, size = 66, normalized size = 2.20 \begin {gather*} \frac {10 \, {\left (\log \relax (x) + 1\right )} e^{\left (2 \, x\right )} + {\left (5 \, \log \relax (x)^{2} + x + 10 \, \log \relax (x) + 7\right )} e^{x} + 3 \, x + 4 \, e^{\left (3 \, x\right )}}{10 \, {\left (\log \relax (x) + 1\right )} e^{x} + 5 \, \log \relax (x)^{2} + x + 4 \, e^{\left (2 \, x\right )} + 10 \, \log \relax (x) + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp(x)^3+300*exp(x)^2+(10*x+170)*exp(x)+
15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+
(8*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+(100*exp(x)+100)*log(x)^3+(140*exp
(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80*exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+8
0*exp(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="maxima")

[Out]

(10*(log(x) + 1)*e^(2*x) + (5*log(x)^2 + x + 10*log(x) + 7)*e^x + 3*x + 4*e^(3*x))/(10*(log(x) + 1)*e^x + 5*lo
g(x)^2 + x + 4*e^(2*x) + 10*log(x) + 7)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {25\,{\mathrm {e}}^x\,{\ln \relax (x)}^4+\left (100\,{\mathrm {e}}^{2\,x}+100\,{\mathrm {e}}^x\right )\,{\ln \relax (x)}^3+\left (300\,{\mathrm {e}}^{2\,x}+140\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^x\,\left (10\,x+170\right )+15\right )\,{\ln \relax (x)}^2+\left (280\,{\mathrm {e}}^{3\,x}+80\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^x\,\left (10\,x-170\right )+{\mathrm {e}}^{2\,x}\,\left (20\,x+340\right )\right )\,\ln \relax (x)+80\,{\mathrm {e}}^{4\,x}+16\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^x\,\left (x^2-16\,x+49\right )-{\mathrm {e}}^{2\,x}\,\left (4\,x-152\right )+{\mathrm {e}}^{3\,x}\,\left (8\,x+156\right )-9}{14\,x+80\,{\mathrm {e}}^{3\,x}+16\,{\mathrm {e}}^{4\,x}+\ln \relax (x)\,\left (20\,x+280\,{\mathrm {e}}^{2\,x}+80\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^x\,\left (20\,x+340\right )+140\right )+{\ln \relax (x)}^3\,\left (100\,{\mathrm {e}}^x+100\right )+25\,{\ln \relax (x)}^4+{\mathrm {e}}^x\,\left (20\,x+140\right )+{\ln \relax (x)}^2\,\left (10\,x+140\,{\mathrm {e}}^{2\,x}+300\,{\mathrm {e}}^x+170\right )+{\mathrm {e}}^{2\,x}\,\left (8\,x+156\right )+x^2+49} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((80*exp(4*x) + 16*exp(5*x) + log(x)*(280*exp(3*x) + 80*exp(4*x) - exp(x)*(10*x - 170) + exp(2*x)*(20*x + 3
40)) + exp(x)*(x^2 - 16*x + 49) + 25*exp(x)*log(x)^4 + log(x)^2*(300*exp(2*x) + 140*exp(3*x) + exp(x)*(10*x +
170) + 15) - exp(2*x)*(4*x - 152) + exp(3*x)*(8*x + 156) + log(x)^3*(100*exp(2*x) + 100*exp(x)) - 9)/(14*x + 8
0*exp(3*x) + 16*exp(4*x) + log(x)*(20*x + 280*exp(2*x) + 80*exp(3*x) + exp(x)*(20*x + 340) + 140) + log(x)^3*(
100*exp(x) + 100) + 25*log(x)^4 + exp(x)*(20*x + 140) + log(x)^2*(10*x + 140*exp(2*x) + 300*exp(x) + 170) + ex
p(2*x)*(8*x + 156) + x^2 + 49),x)

[Out]

int((80*exp(4*x) + 16*exp(5*x) + log(x)*(280*exp(3*x) + 80*exp(4*x) - exp(x)*(10*x - 170) + exp(2*x)*(20*x + 3
40)) + exp(x)*(x^2 - 16*x + 49) + 25*exp(x)*log(x)^4 + log(x)^2*(300*exp(2*x) + 140*exp(3*x) + exp(x)*(10*x +
170) + 15) - exp(2*x)*(4*x - 152) + exp(3*x)*(8*x + 156) + log(x)^3*(100*exp(2*x) + 100*exp(x)) - 9)/(14*x + 8
0*exp(3*x) + 16*exp(4*x) + log(x)*(20*x + 280*exp(2*x) + 80*exp(3*x) + exp(x)*(20*x + 340) + 140) + log(x)^3*(
100*exp(x) + 100) + 25*log(x)^4 + exp(x)*(20*x + 140) + log(x)^2*(10*x + 140*exp(2*x) + 300*exp(x) + 170) + ex
p(2*x)*(8*x + 156) + x^2 + 49), x)

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sympy [A]  time = 0.56, size = 37, normalized size = 1.23 \begin {gather*} \frac {3 x}{x + \left (10 \log {\relax (x )} + 10\right ) e^{x} + 4 e^{2 x} + 5 \log {\relax (x )}^{2} + 10 \log {\relax (x )} + 7} + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*exp(x)*ln(x)**4+(100*exp(x)**2+100*exp(x))*ln(x)**3+(140*exp(x)**3+300*exp(x)**2+(10*x+170)*exp(
x)+15)*ln(x)**2+(80*exp(x)**4+280*exp(x)**3+(20*x+340)*exp(x)**2+(-10*x+170)*exp(x))*ln(x)+16*exp(x)**5+80*exp
(x)**4+(8*x+156)*exp(x)**3+(-4*x+152)*exp(x)**2+(x**2-16*x+49)*exp(x)-9)/(25*ln(x)**4+(100*exp(x)+100)*ln(x)**
3+(140*exp(x)**2+300*exp(x)+10*x+170)*ln(x)**2+(80*exp(x)**3+280*exp(x)**2+(20*x+340)*exp(x)+20*x+140)*ln(x)+1
6*exp(x)**4+80*exp(x)**3+(8*x+156)*exp(x)**2+(20*x+140)*exp(x)+x**2+14*x+49),x)

[Out]

3*x/(x + (10*log(x) + 10)*exp(x) + 4*exp(2*x) + 5*log(x)**2 + 10*log(x) + 7) + exp(x)

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