3.66.9 \(\int \frac {-50-120 x-212 x^2-136 x^3-48 x^4-4 x^5+e^3 (-50 x-40 x^2-4 x^3)+(-50 x-40 x^2-4 x^3) \log (x)}{25 x^3+45 x^4+49 x^5+24 x^6+4 x^7+e^3 (25 x^3+20 x^4+4 x^5)+(25 x^3+20 x^4+4 x^5) \log (x)+(50 x^2+80 x^3+84 x^4+34 x^5+4 x^6+e^3 (50 x^2+30 x^3+4 x^4)+(50 x^2+30 x^3+4 x^4) \log (x)) \log (1+e^3+x+x^2+\log (x))+(25 x+35 x^2+36 x^3+11 x^4+x^5+e^3 (25 x+10 x^2+x^3)+(25 x+10 x^2+x^3) \log (x)) \log ^2(1+e^3+x+x^2+\log (x))} \, dx\)

Optimal. Leaf size=27 \[ \frac {2}{x+\frac {x^2}{5+x}+\log \left (1+e^3+x+x^2+\log (x)\right )} \]

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Rubi [F]  time = 7.45, 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 {-50-120 x-212 x^2-136 x^3-48 x^4-4 x^5+e^3 \left (-50 x-40 x^2-4 x^3\right )+\left (-50 x-40 x^2-4 x^3\right ) \log (x)}{25 x^3+45 x^4+49 x^5+24 x^6+4 x^7+e^3 \left (25 x^3+20 x^4+4 x^5\right )+\left (25 x^3+20 x^4+4 x^5\right ) \log (x)+\left (50 x^2+80 x^3+84 x^4+34 x^5+4 x^6+e^3 \left (50 x^2+30 x^3+4 x^4\right )+\left (50 x^2+30 x^3+4 x^4\right ) \log (x)\right ) \log \left (1+e^3+x+x^2+\log (x)\right )+\left (25 x+35 x^2+36 x^3+11 x^4+x^5+e^3 \left (25 x+10 x^2+x^3\right )+\left (25 x+10 x^2+x^3\right ) \log (x)\right ) \log ^2\left (1+e^3+x+x^2+\log (x)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-50 - 120*x - 212*x^2 - 136*x^3 - 48*x^4 - 4*x^5 + E^3*(-50*x - 40*x^2 - 4*x^3) + (-50*x - 40*x^2 - 4*x^3
)*Log[x])/(25*x^3 + 45*x^4 + 49*x^5 + 24*x^6 + 4*x^7 + E^3*(25*x^3 + 20*x^4 + 4*x^5) + (25*x^3 + 20*x^4 + 4*x^
5)*Log[x] + (50*x^2 + 80*x^3 + 84*x^4 + 34*x^5 + 4*x^6 + E^3*(50*x^2 + 30*x^3 + 4*x^4) + (50*x^2 + 30*x^3 + 4*
x^4)*Log[x])*Log[1 + E^3 + x + x^2 + Log[x]] + (25*x + 35*x^2 + 36*x^3 + 11*x^4 + x^5 + E^3*(25*x + 10*x^2 + x
^3) + (25*x + 10*x^2 + x^3)*Log[x])*Log[1 + E^3 + x + x^2 + Log[x]]^2),x]

[Out]

-10*(12 + 5*E^3)*Defer[Int][1/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) + (5 + x)*Log[1 + E^3 + x + x^2 + Log
[x]])^2), x] - 50*Defer[Int][1/(x*(1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) + (5 + x)*Log[1 + E^3 + x + x^2 +
Log[x]])^2), x] - 4*(53 + 10*E^3)*Defer[Int][x/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) + (5 + x)*Log[1 + E^
3 + x + x^2 + Log[x]])^2), x] - 4*(34 + E^3)*Defer[Int][x^2/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) + (5 +
x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x] - 48*Defer[Int][x^3/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) + (5
+ x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x] - 4*Defer[Int][x^4/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2*x) +
(5 + x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x] - 50*Defer[Int][Log[x]/((1 + E^3 + x + x^2 + Log[x])*(x*(5 + 2
*x) + (5 + x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x] - 40*Defer[Int][(x*Log[x])/((1 + E^3 + x + x^2 + Log[x])
*(x*(5 + 2*x) + (5 + x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x] - 4*Defer[Int][(x^2*Log[x])/((1 + E^3 + x + x^
2 + Log[x])*(x*(5 + 2*x) + (5 + x)*Log[1 + E^3 + x + x^2 + Log[x]])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-25-5 \left (12+5 e^3\right ) x-2 \left (53+10 e^3\right ) x^2-2 \left (34+e^3\right ) x^3-24 x^4-2 x^5-x \left (25+20 x+2 x^2\right ) \log (x)\right )}{x \left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\\ &=2 \int \frac {-25-5 \left (12+5 e^3\right ) x-2 \left (53+10 e^3\right ) x^2-2 \left (34+e^3\right ) x^3-24 x^4-2 x^5-x \left (25+20 x+2 x^2\right ) \log (x)}{x \left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\\ &=2 \int \left (-\frac {5 \left (12+5 e^3\right )}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {25}{x \left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {2 \left (53+10 e^3\right ) x}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {2 \left (34+e^3\right ) x^2}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {24 x^3}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {2 x^4}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {25 \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {20 x \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}-\frac {2 x^2 \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2}\right ) \, dx\\ &=-\left (4 \int \frac {x^4}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\right )-4 \int \frac {x^2 \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-40 \int \frac {x \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-48 \int \frac {x^3}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-50 \int \frac {1}{x \left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-50 \int \frac {\log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (4 \left (34+e^3\right )\right ) \int \frac {x^2}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (10 \left (12+5 e^3\right )\right ) \int \frac {1}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (4 \left (53+10 e^3\right )\right ) \int \frac {x}{\left (1+e^3+x+x^2+\log (x)\right ) \left (5 x+2 x^2+5 \log \left (1+e^3+x+x^2+\log (x)\right )+x \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\\ &=-\left (4 \int \frac {x^4}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\right )-4 \int \frac {x^2 \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-40 \int \frac {x \log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-48 \int \frac {x^3}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-50 \int \frac {1}{x \left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-50 \int \frac {\log (x)}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (4 \left (34+e^3\right )\right ) \int \frac {x^2}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (10 \left (12+5 e^3\right )\right ) \int \frac {1}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx-\left (4 \left (53+10 e^3\right )\right ) \int \frac {x}{\left (1+e^3+x+x^2+\log (x)\right ) \left (x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.09, size = 31, normalized size = 1.15 \begin {gather*} \frac {2 (5+x)}{x (5+2 x)+(5+x) \log \left (1+e^3+x+x^2+\log (x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-50 - 120*x - 212*x^2 - 136*x^3 - 48*x^4 - 4*x^5 + E^3*(-50*x - 40*x^2 - 4*x^3) + (-50*x - 40*x^2 -
4*x^3)*Log[x])/(25*x^3 + 45*x^4 + 49*x^5 + 24*x^6 + 4*x^7 + E^3*(25*x^3 + 20*x^4 + 4*x^5) + (25*x^3 + 20*x^4
+ 4*x^5)*Log[x] + (50*x^2 + 80*x^3 + 84*x^4 + 34*x^5 + 4*x^6 + E^3*(50*x^2 + 30*x^3 + 4*x^4) + (50*x^2 + 30*x^
3 + 4*x^4)*Log[x])*Log[1 + E^3 + x + x^2 + Log[x]] + (25*x + 35*x^2 + 36*x^3 + 11*x^4 + x^5 + E^3*(25*x + 10*x
^2 + x^3) + (25*x + 10*x^2 + x^3)*Log[x])*Log[1 + E^3 + x + x^2 + Log[x]]^2),x]

[Out]

(2*(5 + x))/(x*(5 + 2*x) + (5 + x)*Log[1 + E^3 + x + x^2 + Log[x]])

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fricas [A]  time = 1.27, size = 31, normalized size = 1.15 \begin {gather*} \frac {2 \, {\left (x + 5\right )}}{2 \, x^{2} + {\left (x + 5\right )} \log \left (x^{2} + x + e^{3} + \log \relax (x) + 1\right ) + 5 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-40*x^2-50*x)*log(x)+(-4*x^3-40*x^2-50*x)*exp(3)-4*x^5-48*x^4-136*x^3-212*x^2-120*x-50)/(((x
^3+10*x^2+25*x)*log(x)+(x^3+10*x^2+25*x)*exp(3)+x^5+11*x^4+36*x^3+35*x^2+25*x)*log(log(x)+exp(3)+x^2+x+1)^2+((
4*x^4+30*x^3+50*x^2)*log(x)+(4*x^4+30*x^3+50*x^2)*exp(3)+4*x^6+34*x^5+84*x^4+80*x^3+50*x^2)*log(log(x)+exp(3)+
x^2+x+1)+(4*x^5+20*x^4+25*x^3)*log(x)+(4*x^5+20*x^4+25*x^3)*exp(3)+4*x^7+24*x^6+49*x^5+45*x^4+25*x^3),x, algor
ithm="fricas")

[Out]

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

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giac [A]  time = 0.45, size = 42, normalized size = 1.56 \begin {gather*} \frac {2 \, {\left (x + 5\right )}}{2 \, x^{2} + x \log \left (x^{2} + x + e^{3} + \log \relax (x) + 1\right ) + 5 \, x + 5 \, \log \left (x^{2} + x + e^{3} + \log \relax (x) + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-40*x^2-50*x)*log(x)+(-4*x^3-40*x^2-50*x)*exp(3)-4*x^5-48*x^4-136*x^3-212*x^2-120*x-50)/(((x
^3+10*x^2+25*x)*log(x)+(x^3+10*x^2+25*x)*exp(3)+x^5+11*x^4+36*x^3+35*x^2+25*x)*log(log(x)+exp(3)+x^2+x+1)^2+((
4*x^4+30*x^3+50*x^2)*log(x)+(4*x^4+30*x^3+50*x^2)*exp(3)+4*x^6+34*x^5+84*x^4+80*x^3+50*x^2)*log(log(x)+exp(3)+
x^2+x+1)+(4*x^5+20*x^4+25*x^3)*log(x)+(4*x^5+20*x^4+25*x^3)*exp(3)+4*x^7+24*x^6+49*x^5+45*x^4+25*x^3),x, algor
ithm="giac")

[Out]

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

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maple [A]  time = 0.07, size = 43, normalized size = 1.59

method	result	size
risch	\(\frac {2 x +10}{x \ln \left (\ln \relax (x )+{\mathrm e}^{3}+x^{2}+x +1\right )+2 x^{2}+5 \ln \left (\ln \relax (x )+{\mathrm e}^{3}+x^{2}+x +1\right )+5 x}\)	\(43\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^3-40*x^2-50*x)*ln(x)+(-4*x^3-40*x^2-50*x)*exp(3)-4*x^5-48*x^4-136*x^3-212*x^2-120*x-50)/(((x^3+10*x
^2+25*x)*ln(x)+(x^3+10*x^2+25*x)*exp(3)+x^5+11*x^4+36*x^3+35*x^2+25*x)*ln(ln(x)+exp(3)+x^2+x+1)^2+((4*x^4+30*x
^3+50*x^2)*ln(x)+(4*x^4+30*x^3+50*x^2)*exp(3)+4*x^6+34*x^5+84*x^4+80*x^3+50*x^2)*ln(ln(x)+exp(3)+x^2+x+1)+(4*x
^5+20*x^4+25*x^3)*ln(x)+(4*x^5+20*x^4+25*x^3)*exp(3)+4*x^7+24*x^6+49*x^5+45*x^4+25*x^3),x,method=_RETURNVERBOS
E)

[Out]

2*(5+x)/(x*ln(ln(x)+exp(3)+x^2+x+1)+2*x^2+5*ln(ln(x)+exp(3)+x^2+x+1)+5*x)

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maxima [A]  time = 0.47, size = 31, normalized size = 1.15 \begin {gather*} \frac {2 \, {\left (x + 5\right )}}{2 \, x^{2} + {\left (x + 5\right )} \log \left (x^{2} + x + e^{3} + \log \relax (x) + 1\right ) + 5 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3-40*x^2-50*x)*log(x)+(-4*x^3-40*x^2-50*x)*exp(3)-4*x^5-48*x^4-136*x^3-212*x^2-120*x-50)/(((x
^3+10*x^2+25*x)*log(x)+(x^3+10*x^2+25*x)*exp(3)+x^5+11*x^4+36*x^3+35*x^2+25*x)*log(log(x)+exp(3)+x^2+x+1)^2+((
4*x^4+30*x^3+50*x^2)*log(x)+(4*x^4+30*x^3+50*x^2)*exp(3)+4*x^6+34*x^5+84*x^4+80*x^3+50*x^2)*log(log(x)+exp(3)+
x^2+x+1)+(4*x^5+20*x^4+25*x^3)*log(x)+(4*x^5+20*x^4+25*x^3)*exp(3)+4*x^7+24*x^6+49*x^5+45*x^4+25*x^3),x, algor
ithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {120\,x+{\mathrm {e}}^3\,\left (4\,x^3+40\,x^2+50\,x\right )+212\,x^2+136\,x^3+48\,x^4+4\,x^5+\ln \relax (x)\,\left (4\,x^3+40\,x^2+50\,x\right )+50}{\ln \left (x+{\mathrm {e}}^3+\ln \relax (x)+x^2+1\right )\,\left (\ln \relax (x)\,\left (4\,x^4+30\,x^3+50\,x^2\right )+{\mathrm {e}}^3\,\left (4\,x^4+30\,x^3+50\,x^2\right )+50\,x^2+80\,x^3+84\,x^4+34\,x^5+4\,x^6\right )+\ln \relax (x)\,\left (4\,x^5+20\,x^4+25\,x^3\right )+{\ln \left (x+{\mathrm {e}}^3+\ln \relax (x)+x^2+1\right )}^2\,\left (25\,x+{\mathrm {e}}^3\,\left (x^3+10\,x^2+25\,x\right )+\ln \relax (x)\,\left (x^3+10\,x^2+25\,x\right )+35\,x^2+36\,x^3+11\,x^4+x^5\right )+{\mathrm {e}}^3\,\left (4\,x^5+20\,x^4+25\,x^3\right )+25\,x^3+45\,x^4+49\,x^5+24\,x^6+4\,x^7} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(120*x + exp(3)*(50*x + 40*x^2 + 4*x^3) + 212*x^2 + 136*x^3 + 48*x^4 + 4*x^5 + log(x)*(50*x + 40*x^2 + 4*
x^3) + 50)/(log(x + exp(3) + log(x) + x^2 + 1)*(log(x)*(50*x^2 + 30*x^3 + 4*x^4) + exp(3)*(50*x^2 + 30*x^3 + 4
*x^4) + 50*x^2 + 80*x^3 + 84*x^4 + 34*x^5 + 4*x^6) + log(x)*(25*x^3 + 20*x^4 + 4*x^5) + log(x + exp(3) + log(x
) + x^2 + 1)^2*(25*x + exp(3)*(25*x + 10*x^2 + x^3) + log(x)*(25*x + 10*x^2 + x^3) + 35*x^2 + 36*x^3 + 11*x^4
+ x^5) + exp(3)*(25*x^3 + 20*x^4 + 4*x^5) + 25*x^3 + 45*x^4 + 49*x^5 + 24*x^6 + 4*x^7),x)

[Out]

int(-(120*x + exp(3)*(50*x + 40*x^2 + 4*x^3) + 212*x^2 + 136*x^3 + 48*x^4 + 4*x^5 + log(x)*(50*x + 40*x^2 + 4*
x^3) + 50)/(log(x + exp(3) + log(x) + x^2 + 1)*(log(x)*(50*x^2 + 30*x^3 + 4*x^4) + exp(3)*(50*x^2 + 30*x^3 + 4
*x^4) + 50*x^2 + 80*x^3 + 84*x^4 + 34*x^5 + 4*x^6) + log(x)*(25*x^3 + 20*x^4 + 4*x^5) + log(x + exp(3) + log(x
) + x^2 + 1)^2*(25*x + exp(3)*(25*x + 10*x^2 + x^3) + log(x)*(25*x + 10*x^2 + x^3) + 35*x^2 + 36*x^3 + 11*x^4
+ x^5) + exp(3)*(25*x^3 + 20*x^4 + 4*x^5) + 25*x^3 + 45*x^4 + 49*x^5 + 24*x^6 + 4*x^7), x)

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sympy [A]  time = 0.57, size = 31, normalized size = 1.15 \begin {gather*} \frac {2 x + 10}{2 x^{2} + 5 x + \left (x + 5\right ) \log {\left (x^{2} + x + \log {\relax (x )} + 1 + e^{3} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**3-40*x**2-50*x)*ln(x)+(-4*x**3-40*x**2-50*x)*exp(3)-4*x**5-48*x**4-136*x**3-212*x**2-120*x-5
0)/(((x**3+10*x**2+25*x)*ln(x)+(x**3+10*x**2+25*x)*exp(3)+x**5+11*x**4+36*x**3+35*x**2+25*x)*ln(ln(x)+exp(3)+x
**2+x+1)**2+((4*x**4+30*x**3+50*x**2)*ln(x)+(4*x**4+30*x**3+50*x**2)*exp(3)+4*x**6+34*x**5+84*x**4+80*x**3+50*
x**2)*ln(ln(x)+exp(3)+x**2+x+1)+(4*x**5+20*x**4+25*x**3)*ln(x)+(4*x**5+20*x**4+25*x**3)*exp(3)+4*x**7+24*x**6+
49*x**5+45*x**4+25*x**3),x)

[Out]

(2*x + 10)/(2*x**2 + 5*x + (x + 5)*log(x**2 + x + log(x) + 1 + exp(3)))

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