3.77.81 \(\int \frac {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} (2 e^{e^5}-2 x-6 x^2)+(8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} (-3 e^{e^5}-3 x-3 x^2)) \log (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} (2 x+2 x^2)})}{(2 e^{e^5}+2 x+2 x^2) \log ^2(\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} (2 x+2 x^2)})} \, dx\)

Optimal. Leaf size=30 \[ \frac {x \left (4-\sqrt [4]{x^2}\right )}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \]

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Rubi [F]  time = 10.96, 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 {-8 e^{e^5}+8 x+24 x^2+\sqrt [4]{x^2} \left (2 e^{e^5}-2 x-6 x^2\right )+\left (8 e^{e^5}+8 x+8 x^2+\sqrt [4]{x^2} \left (-3 e^{e^5}-3 x-3 x^2\right )\right ) \log \left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )}{\left (2 e^{e^5}+2 x+2 x^2\right ) \log ^2\left (\frac {x}{e^{2 e^5}+x^2+2 x^3+x^4+e^{e^5} \left (2 x+2 x^2\right )}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8*E^E^5 + 8*x + 24*x^2 + (x^2)^(1/4)*(2*E^E^5 - 2*x - 6*x^2) + (8*E^E^5 + 8*x + 8*x^2 + (x^2)^(1/4)*(-3*
E^E^5 - 3*x - 3*x^2))*Log[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))])/((2*E^E^5 + 2*x + 2*x^2)*L
og[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))]^2),x]

[Out]

12*Defer[Int][Log[x/(E^E^5 + x + x^2)^2]^(-2), x] - ((32*I)*E^E^5*Defer[Int][1/((-1 + I*Sqrt[-1 + 4*E^E^5] - 2
*x)*Log[x/(E^E^5 + x + x^2)^2]^2), x])/Sqrt[-1 + 4*E^E^5] - 8*(1 + I/Sqrt[-1 + 4*E^E^5])*Defer[Int][1/((1 - I*
Sqrt[-1 + 4*E^E^5] + 2*x)*Log[x/(E^E^5 + x + x^2)^2]^2), x] - ((32*I)*E^E^5*Defer[Int][1/((1 + I*Sqrt[-1 + 4*E
^E^5] + 2*x)*Log[x/(E^E^5 + x + x^2)^2]^2), x])/Sqrt[-1 + 4*E^E^5] - 8*(1 - I/Sqrt[-1 + 4*E^E^5])*Defer[Int][1
/((1 + I*Sqrt[-1 + 4*E^E^5] + 2*x)*Log[x/(E^E^5 + x + x^2)^2]^2), x] + 4*Defer[Int][Log[x/(E^E^5 + x + x^2)^2]
^(-1), x] + (4*(x^2)^(1/4)*Defer[Subst][Defer[Int][Log[x^2/(E^E^5 + x^2 + x^4)^2]^(-2), x], x, Sqrt[x]])/Sqrt[
x] - (6*(x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/Log[x^2/(E^E^5 + x^2 + x^4)^2]^2, x], x, Sqrt[x]])/Sqrt[x] - (
(1 - I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x
)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]]*Sqrt[x]) - (E^E^5*(1 -
I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*Log
[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]]*Sqrt[x]) + (3*(1 - E^E^5)*(1
- I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*
Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]]*Sqrt[x]) + ((4*I)*E^E^5*(
x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4
)^2]^2), x], x, Sqrt[x]])/(Sqrt[(1 - 4*E^E^5)*(1 + I*Sqrt[-1 + 4*E^E^5])]*Sqrt[x]) + (I*Sqrt[(1 - I*Sqrt[-1 +
4*E^E^5])/(1 - 4*E^E^5)]*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*
Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] + (I*E^E^5*Sqrt[(1 - I*Sqrt[-1 + 4*E^E^5])/(1 - 4*
E^E^5)]*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*Log[x^2/(E^E^5 +
x^2 + x^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] - ((3*I)*(1 - E^E^5)*Sqrt[(1 - I*Sqrt[-1 + 4*E^E^5])/(1 - 4*E^E^5)]
*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]] - Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x
^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] - ((4*I)*E^E^5*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1
+ 4*E^E^5]] - Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[(-I)*(1 - 4*E^E^5)*(I + Sq
rt[-1 + 4*E^E^5])]*Sqrt[x]) - ((1 - I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*
Sqrt[-1 + 4*E^E^5]] + Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*
E^E^5]]*Sqrt[x]) - (E^E^5*(1 - I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[
-1 + 4*E^E^5]] + Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5
]]*Sqrt[x]) + (3*(1 - E^E^5)*(1 - I/Sqrt[-1 + 4*E^E^5])*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sq
rt[-1 + 4*E^E^5]] + Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[-1 - I*Sqrt[-1 + 4*E^
E^5]]*Sqrt[x]) + ((4*I)*E^E^5*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[-1 + 4*E^E^5]] + Sqrt[2
]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(Sqrt[(1 - 4*E^E^5)*(1 + I*Sqrt[-1 + 4*E^E^5])]*Sqrt[
x]) + (I*Sqrt[(1 - I*Sqrt[-1 + 4*E^E^5])/(1 - 4*E^E^5)]*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sq
rt[-1 + 4*E^E^5]] + Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] + (I*E^E^5*Sqrt[(1
- I*Sqrt[-1 + 4*E^E^5])/(1 - 4*E^E^5)]*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]]
+ Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] - ((3*I)*(1 - E^E^5)*Sqrt[(1 - I*Sqr
t[-1 + 4*E^E^5])/(1 - 4*E^E^5)]*(x^2)^(1/4)*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]] + Sqrt
[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/Sqrt[x] - ((4*I)*E^E^5*(x^2)^(1/4)*Defer[Subst][Def
er[Int][1/((Sqrt[-1 + I*Sqrt[-1 + 4*E^E^5]] + Sqrt[2]*x)*Log[x^2/(E^E^5 + x^2 + x^4)^2]^2), x], x, Sqrt[x]])/(
Sqrt[(-I)*(1 - 4*E^E^5)*(I + Sqrt[-1 + 4*E^E^5])]*Sqrt[x]) - (3*(x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/Log[x^
2/(E^E^5 + x^2 + x^4)^2], x], x, Sqrt[x]])/Sqrt[x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\frac {2 \left (-e^{e^5}+x+3 x^2\right ) \left (-4+\sqrt [4]{x^2}\right )}{e^{e^5}+x+x^2}-\left (-8+3 \sqrt [4]{x^2}\right ) \log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}{2 \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx\\ &=\frac {1}{2} \int \frac {-\frac {2 \left (-e^{e^5}+x+3 x^2\right ) \left (-4+\sqrt [4]{x^2}\right )}{e^{e^5}+x+x^2}-\left (-8+3 \sqrt [4]{x^2}\right ) \log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}{\log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx\\ &=\frac {1}{2} \int \left (\frac {2 e^{e^5} \sqrt [4]{x^2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}-\frac {2 x \sqrt [4]{x^2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}-\frac {6 \left (x^2\right )^{5/4}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}-\frac {8 \left (e^{e^5}-x-3 x^2\right )}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}+\frac {8}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}-\frac {3 \sqrt [4]{x^2}}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}\right ) \, dx\\ &=-\left (\frac {3}{2} \int \frac {\sqrt [4]{x^2}}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx\right )-3 \int \frac {\left (x^2\right )^{5/4}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-4 \int \frac {e^{e^5}-x-3 x^2}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx+4 \int \frac {1}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx+e^{e^5} \int \frac {\sqrt [4]{x^2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-\int \frac {x \sqrt [4]{x^2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx\\ &=-\left (4 \int \left (-\frac {3}{\log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}+\frac {2 \left (2 e^{e^5}+x\right )}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}\right ) \, dx\right )+4 \int \frac {1}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-\frac {\sqrt [4]{x^2} \int \frac {x^{3/2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx}{\sqrt {x}}-\frac {\left (3 \sqrt [4]{x^2}\right ) \int \frac {\sqrt {x}}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx}{2 \sqrt {x}}-\frac {\left (3 \sqrt [4]{x^2}\right ) \int \frac {x^{5/2}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx}{\sqrt {x}}+\frac {\left (e^{e^5} \sqrt [4]{x^2}\right ) \int \frac {\sqrt {x}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx}{\sqrt {x}}\\ &=4 \int \frac {1}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-8 \int \frac {2 e^{e^5}+x}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx+12 \int \frac {1}{\log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-\frac {\left (2 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \frac {x^4}{\left (e^{e^5}+x^2+x^4\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {\left (3 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\log \left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {\left (6 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (e^{e^5}+x^2+x^4\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {\left (2 e^{e^5} \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (e^{e^5}+x^2+x^4\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {x}}\\ &=4 \int \frac {1}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-8 \int \left (\frac {2 e^{e^5}}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}+\frac {x}{\left (e^{e^5}+x+x^2\right ) \log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )}\right ) \, dx+12 \int \frac {1}{\log ^2\left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \, dx-\frac {\left (2 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{\log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}-\frac {e^{e^5}+x^2}{\left (e^{e^5}+x^2+x^4\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}\right ) \, dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {\left (3 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\log \left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )} \, dx,x,\sqrt {x}\right )}{\sqrt {x}}-\frac {\left (6 \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \left (-\frac {1}{\log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}+\frac {x^2}{\log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}+\frac {e^{e^5}+\left (1-e^{e^5}\right ) x^2}{\left (e^{e^5}+x^2+x^4\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}\right ) \, dx,x,\sqrt {x}\right )}{\sqrt {x}}+\frac {\left (2 e^{e^5} \sqrt [4]{x^2}\right ) \operatorname {Subst}\left (\int \left (\frac {1+\frac {i}{\sqrt {-1+4 e^{e^5}}}}{\left (1-i \sqrt {-1+4 e^{e^5}}+2 x^2\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}+\frac {1-\frac {i}{\sqrt {-1+4 e^{e^5}}}}{\left (1+i \sqrt {-1+4 e^{e^5}}+2 x^2\right ) \log ^2\left (\frac {x^2}{\left (e^{e^5}+x^2+x^4\right )^2}\right )}\right ) \, dx,x,\sqrt {x}\right )}{\sqrt {x}}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 29, normalized size = 0.97 \begin {gather*} -\frac {x \left (-4+\sqrt [4]{x^2}\right )}{\log \left (\frac {x}{\left (e^{e^5}+x+x^2\right )^2}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*E^E^5 + 8*x + 24*x^2 + (x^2)^(1/4)*(2*E^E^5 - 2*x - 6*x^2) + (8*E^E^5 + 8*x + 8*x^2 + (x^2)^(1/4
)*(-3*E^E^5 - 3*x - 3*x^2))*Log[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))])/((2*E^E^5 + 2*x + 2*
x^2)*Log[x/(E^(2*E^5) + x^2 + 2*x^3 + x^4 + E^E^5*(2*x + 2*x^2))]^2),x]

[Out]

-((x*(-4 + (x^2)^(1/4)))/Log[x/(E^E^5 + x + x^2)^2])

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fricas [A]  time = 0.59, size = 47, normalized size = 1.57 \begin {gather*} -\frac {{\left (x^{2}\right )}^{\frac {1}{4}} x - 4 \, x}{\log \left (\frac {x}{x^{4} + 2 \, x^{3} + x^{2} + 2 \, {\left (x^{2} + x\right )} e^{\left (e^{5}\right )} + e^{\left (2 \, e^{5}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*log(x/(exp(exp(5))^2+(2*x^2+2*x)*e
xp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^
2+2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, algorithm="fricas")

[Out]

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

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*log(x/(exp(exp(5))^2+(2*x^2+2*x)*e
xp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^
2+2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Ch
eck [abs(sa

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maple [F]  time = 0.20, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-3 \,{\mathrm e}^{{\mathrm e}^{5}}-3 x^{2}-3 x \right ) \left (x^{2}\right )^{\frac {1}{4}}+8 \,{\mathrm e}^{{\mathrm e}^{5}}+8 x^{2}+8 x \right ) \ln \left (\frac {x}{{\mathrm e}^{2 \,{\mathrm e}^{5}}+\left (2 x^{2}+2 x \right ) {\mathrm e}^{{\mathrm e}^{5}}+x^{4}+2 x^{3}+x^{2}}\right )+\left (2 \,{\mathrm e}^{{\mathrm e}^{5}}-6 x^{2}-2 x \right ) \left (x^{2}\right )^{\frac {1}{4}}-8 \,{\mathrm e}^{{\mathrm e}^{5}}+24 x^{2}+8 x}{\left (2 \,{\mathrm e}^{{\mathrm e}^{5}}+2 x^{2}+2 x \right ) \ln \left (\frac {x}{{\mathrm e}^{2 \,{\mathrm e}^{5}}+\left (2 x^{2}+2 x \right ) {\mathrm e}^{{\mathrm e}^{5}}+x^{4}+2 x^{3}+x^{2}}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*ln(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(
5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+2*x)/
ln(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x)

[Out]

int((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*ln(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(
5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^2+2*x)/
ln(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*exp(exp(5))-3*x^2-3*x)*(x^2)^(1/4)+8*exp(exp(5))+8*x^2+8*x)*log(x/(exp(exp(5))^2+(2*x^2+2*x)*e
xp(exp(5))+x^4+2*x^3+x^2))+(2*exp(exp(5))-6*x^2-2*x)*(x^2)^(1/4)-8*exp(exp(5))+24*x^2+8*x)/(2*exp(exp(5))+2*x^
2+2*x)/log(x/(exp(exp(5))^2+(2*x^2+2*x)*exp(exp(5))+x^4+2*x^3+x^2))^2,x, algorithm="maxima")

[Out]

-(4*x^3*e^(e^5) + 3*(x^3 + x^2 + x*e^(e^5))*x^(5/2) - 12*(x^3 + x^2 + x*e^(e^5))*x^2 + 4*x^2*e^(e^5) + (x^3 +
x^2 + x*e^(e^5))*x^(3/2) - 4*(x^3 + x^2 + x*e^(e^5))*x + 4*x*e^(2*e^5) - (x^3*e^(e^5) + x^2*e^(e^5) + x*e^(2*e
^5))*sqrt(x))/((3*x^2 + x - e^(e^5))*x^2*log(x) + (3*x^2 + x - e^(e^5))*x*log(x) - 2*((3*x^2 + x - e^(e^5))*x^
2 + 3*x^2*e^(e^5) + (3*x^2 + x - e^(e^5))*x + x*e^(e^5) - e^(2*e^5))*log(x^2 + x + e^(e^5)) + (3*x^2*e^(e^5) +
x*e^(e^5) - e^(2*e^5))*log(x)) - 1/2*integrate(-2*(3*(x^3 - x^2*(2*e^(e^5) - 1) - x*e^(e^5) - 2*e^(2*e^5))*x^
(9/2) + 8*(x^2*(6*e^(e^5) - 1) + 2*x*e^(e^5) + 2*e^(2*e^5))*x^4 + 48*x^4*e^(2*e^5) - (3*x^4 - 6*x^3 - x^2*(2*e
^(e^5) + 5) + 2*x*e^(e^5) + 11*e^(2*e^5))*x^(7/2) - 16*(x^3 - x^2*(2*e^(e^5) - 1) - x*e^(e^5) - 2*e^(2*e^5))*x
^3 + 32*x^3*e^(2*e^5) + (3*x^4*(2*e^(e^5) - 3) + x^3*(22*e^(e^5) - 5) + 12*x^2*(2*e^(2*e^5) + e^(e^5)) + x*(2*
e^(2*e^5) + e^(e^5)) - 14*e^(3*e^5) - 3*e^(2*e^5))*x^(5/2) - 8*(3*x^4*(2*e^(e^5) - 1) + 2*x^3*(6*e^(e^5) - 1)
+ 4*x^2*(2*e^(2*e^5) + e^(e^5)) - 6*e^(3*e^5) - e^(2*e^5))*x^2 - 8*x^2*(6*e^(3*e^5) - e^(2*e^5)) - (21*x^4*e^(
e^5) + 10*x^3*e^(e^5) - x^2*(22*e^(2*e^5) - e^(e^5)) - 6*x*e^(2*e^5) + 5*e^(3*e^5))*x^(3/2) + 16*(3*x^4*e^(e^5
) + x^3*e^(e^5) - 4*x^2*e^(2*e^5) - x*e^(2*e^5) + e^(3*e^5))*x - 16*x*e^(3*e^5) - (18*x^4*e^(2*e^5) + 13*x^3*e
^(2*e^5) - x^2*(14*e^(3*e^5) - 3*e^(2*e^5)) - 5*x*e^(3*e^5))*sqrt(x))/((9*x^4 + 6*x^3 - x^2*(6*e^(e^5) - 1) -
2*x*e^(e^5) + e^(2*e^5))*x^4*log(x) + 2*(9*x^4 + 6*x^3 - x^2*(6*e^(e^5) - 1) - 2*x*e^(e^5) + e^(2*e^5))*x^3*lo
g(x) + (9*x^4*(2*e^(e^5) + 1) + 6*x^3*(2*e^(e^5) + 1) - x^2*(12*e^(2*e^5) + 4*e^(e^5) - 1) - 2*x*(2*e^(2*e^5)
+ e^(e^5)) + 2*e^(3*e^5) + e^(2*e^5))*x^2*log(x) + 2*(9*x^4*e^(e^5) + 6*x^3*e^(e^5) - x^2*(6*e^(2*e^5) - e^(e^
5)) - 2*x*e^(2*e^5) + e^(3*e^5))*x*log(x) - 2*((9*x^4 + 6*x^3 - x^2*(6*e^(e^5) - 1) - 2*x*e^(e^5) + e^(2*e^5))
*x^4 + 9*x^4*e^(2*e^5) + 2*(9*x^4 + 6*x^3 - x^2*(6*e^(e^5) - 1) - 2*x*e^(e^5) + e^(2*e^5))*x^3 + 6*x^3*e^(2*e^
5) + (9*x^4*(2*e^(e^5) + 1) + 6*x^3*(2*e^(e^5) + 1) - x^2*(12*e^(2*e^5) + 4*e^(e^5) - 1) - 2*x*(2*e^(2*e^5) +
e^(e^5)) + 2*e^(3*e^5) + e^(2*e^5))*x^2 - x^2*(6*e^(3*e^5) - e^(2*e^5)) + 2*(9*x^4*e^(e^5) + 6*x^3*e^(e^5) - x
^2*(6*e^(2*e^5) - e^(e^5)) - 2*x*e^(2*e^5) + e^(3*e^5))*x - 2*x*e^(3*e^5) + e^(4*e^5))*log(x^2 + x + e^(e^5))
+ (9*x^4*e^(2*e^5) + 6*x^3*e^(2*e^5) - x^2*(6*e^(3*e^5) - e^(2*e^5)) - 2*x*e^(3*e^5) + e^(4*e^5))*log(x)), x)

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mupad [B]  time = 6.51, size = 3644, normalized size = 121.47 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x - 8*exp(exp(5)) - (x^2)^(1/4)*(2*x - 2*exp(exp(5)) + 6*x^2) + log(x/(exp(2*exp(5)) + exp(exp(5))*(2*x
+ 2*x^2) + x^2 + 2*x^3 + x^4))*(8*x + 8*exp(exp(5)) - (x^2)^(1/4)*(3*x + 3*exp(exp(5)) + 3*x^2) + 8*x^2) + 24
*x^2)/(log(x/(exp(2*exp(5)) + exp(exp(5))*(2*x + 2*x^2) + x^2 + 2*x^3 + x^4))^2*(2*x + 2*exp(exp(5)) + 2*x^2))
,x)

[Out]

(x/2 + 1/3)*(x^2)^(1/4) - ((x*((exp(exp(5))*((5832*exp(exp(5)) + 486)/(108*(12*exp(exp(5)) + 1)^2) - (exp(exp(
5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(5832*exp(exp(5))
+ 486))/(216*(12*exp(exp(5)) + 1)^2)))/3 + (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(648*(12*exp(exp(5)) + 1
)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(1944*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(90*exp(exp(5)
) - 39)*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(5832*ex
p(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))
/(2916*(12*exp(exp(5)) + 1)^2)))/3 - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5))
+ 1)^2) + (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/27 + (5832*exp(exp(5)) +
486)/(972*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*((5832*exp(exp(5)) + 486)/(36*(12*exp(exp(5)) + 1)^2) + (13*e
xp(-exp(5))*(1944*exp(exp(5)) + 162))/(216*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486)
)/(648*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(972*(12*exp(ex
p(5)) + 1)^2)))/9 - exp(exp(5))*((exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1
)^2) + (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/9 - (5832*exp(exp(5)) + 486)/
(324*(12*exp(exp(5)) + 1)^2) - (exp(exp(5))*((5832*exp(exp(5)) + 486)/(36*(12*exp(exp(5)) + 1)^2) + (13*exp(-e
xp(5))*(1944*exp(exp(5)) + 162))/(216*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(64
8*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5))
+ 1)^2)))/3 - (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(1944*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(58
32*exp(exp(5)) + 486))/(5832*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(27*exp(2*exp(5)) + 6*exp(exp(5)))*(5832*
exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(1944*exp(exp(5)) + 16
2))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(1944*exp(exp(5)) + 162))/(2916*(12*exp
(exp(5)) + 1)^2) - (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(5832*exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2
) + (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)^2)) - (exp(exp(5)
)*(1944*exp(exp(5)) + 162))/(72*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(
exp(5)) + 1)^2) + (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(5832*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*
(5832*exp(exp(5)) + 486))/(17496*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(27*exp(2*exp(5)) + 6*exp(exp(5)))*(1
944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(27*exp(2*exp(5)) + 6*exp(exp(5)))*(5832*
exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(1944*exp(exp(5)) + 1
62))/(2916*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(90*exp(exp(5)) - 39)*(1944*exp(exp(5)) + 162))/(8748*(12*e
xp(exp(5)) + 1)^2) + (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(5832*exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)
^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(26244*(12*exp(exp(5)) + 1)^2)) - exp(exp(
5))*((exp(exp(5))*((5832*exp(exp(5)) + 486)/(108*(12*exp(exp(5)) + 1)^2) - (exp(exp(5))*((exp(-exp(5))*(1944*e
xp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5
)) + 1)^2)))/3 + (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(648*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5
832*exp(exp(5)) + 486))/(1944*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(90*exp(exp(5)) - 39)*(1944*exp(exp(5))
+ 162))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(5832*exp(exp(5)) + 486))/(972*(12
*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1
)^2)))/3 - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(12*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5)
)*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2)))/27 + (5832*exp(exp(5)) + 486)/(972*(12*exp(exp(5))
+ 1)^2) + (exp(exp(5))*((5832*exp(exp(5)) + 486)/(36*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(1944*exp(exp(
5)) + 162))/(216*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(648*(12*exp(exp(5)) + 1
)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2)))/9 + (exp(e
xp(5))*(5832*exp(exp(5)) + 486))/(216*(12*exp(exp(5)) + 1)^2) + (13*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(58
32*(12*exp(exp(5)) + 1)^2) - (13*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(17496*(12*exp(exp(5)) + 1)^2) + (exp(
-exp(5))*(27*exp(2*exp(5)) + 6*exp(exp(5)))*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp
(5))*(27*exp(2*exp(5)) + 6*exp(exp(5)))*(5832*exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5)
)*(51*exp(exp(5)) - 9/2)*(1944*exp(exp(5)) + 162))/(2916*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(90*exp(exp(5
)) - 39)*(1944*exp(exp(5)) + 162))/(8748*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(51*exp(exp(5)) - 9/2)*(5832*
exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(90*exp(exp(5)) - 39)*(5832*exp(exp(5)) + 48
6))/(26244*(12*exp(exp(5)) + 1)^2)))*(x^2)^(1/4) - x*((exp(exp(5))*((5832*exp(exp(5)) + 486)/(81*(12*exp(exp(5
)) + 1)^2) - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(9*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5)
)*(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2)))/3 + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(243*(
12*exp(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(729*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5)
)*(204*exp(exp(5)) - 44)*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(88*exp(exp(5)
) - 4)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp
(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2)))/3 - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(9*
(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2)))/27 - exp(exp
(5))*((exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(9*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(5832
*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2)))/9 - (5832*exp(exp(5)) + 486)/(243*(12*exp(exp(5)) + 1)^2) -
(exp(exp(5))*((5832*exp(exp(5)) + 486)/(27*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162)
)/(81*(12*exp(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(243*(12*exp(exp(5)) + 1)^2) - (exp(
-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2)))/3 - (4*exp(-exp(5))*(
1944*exp(exp(5)) + 162))/(729*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(2187*(12*ex
p(exp(5)) + 1)^2) + (exp(-exp(5))*(88*exp(exp(5)) - 4)*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2)
- (exp(-exp(5))*(204*exp(exp(5)) - 44)*(1944*exp(exp(5)) + 162))/(2916*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))
*(88*exp(exp(5)) - 4)*(5832*exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(204*exp(exp(5))
- 44)*(5832*exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(5832*exp(exp(5)) + 486)*(36*ex
p(2*exp(5)) + 8*exp(exp(5)) + 6*exp(exp(5))*(4*exp(exp(5)) - 2/3)))/(972*(12*exp(exp(5)) + 1)^2)) + (5832*exp(
exp(5)) + 486)/(729*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*((5832*exp(exp(5)) + 486)/(27*(12*exp(exp(5)) + 1)^
2) + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(81*(12*exp(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp(exp(5))
+ 486))/(243*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp(exp(5)) + 486))/(972*(1
2*exp(exp(5)) + 1)^2)))/9 - (exp(exp(5))*(1944*exp(exp(5)) + 162))/(27*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*
(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(2187*(12*ex
p(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(6561*(12*exp(exp(5)) + 1)^2) - (exp(2*exp(5))*(
5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(88*exp(exp(5)) - 4)*(1944*exp(exp(5)) +
162))/(2916*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(204*exp(exp(5)) - 44)*(1944*exp(exp(5)) + 162))/(8748*(12
*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(88*exp(exp(5)) - 4)*(5832*exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)
^2) - (exp(-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp(exp(5)) + 486))/(26244*(12*exp(exp(5)) + 1)^2) + (exp(-ex
p(5))*(1944*exp(exp(5)) + 162)*(36*exp(2*exp(5)) + 8*exp(exp(5)) + 6*exp(exp(5))*(4*exp(exp(5)) - 2/3)))/(972*
(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(5832*exp(exp(5)) + 486)*(36*exp(2*exp(5)) + 8*exp(exp(5)) + 6*exp(exp
(5))*(4*exp(exp(5)) - 2/3)))/(2916*(12*exp(exp(5)) + 1)^2)) + exp(exp(5))*((exp(exp(5))*((5832*exp(exp(5)) + 4
86)/(81*(12*exp(exp(5)) + 1)^2) - (exp(exp(5))*((exp(-exp(5))*(1944*exp(exp(5)) + 162))/(9*(12*exp(exp(5)) + 1
)^2) + (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) + 1)^2)))/3 + (4*exp(-exp(5))*(1944*exp(e
xp(5)) + 162))/(243*(12*exp(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(729*(12*exp(exp(5)) +
1)^2) + (exp(-exp(5))*(204*exp(exp(5)) - 44)*(1944*exp(exp(5)) + 162))/(972*(12*exp(exp(5)) + 1)^2) + (exp(-e
xp(5))*(88*exp(exp(5)) - 4)*(5832*exp(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(204*exp(ex
p(5)) - 44)*(5832*exp(exp(5)) + 486))/(2916*(12*exp(exp(5)) + 1)^2)))/3 - (exp(exp(5))*((exp(-exp(5))*(1944*ex
p(exp(5)) + 162))/(9*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5)) +
1)^2)))/27 + (5832*exp(exp(5)) + 486)/(729*(12*exp(exp(5)) + 1)^2) + (exp(exp(5))*((5832*exp(exp(5)) + 486)/(
27*(12*exp(exp(5)) + 1)^2) + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(81*(12*exp(exp(5)) + 1)^2) - (4*exp(-e
xp(5))*(5832*exp(exp(5)) + 486))/(243*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp
(exp(5)) + 486))/(972*(12*exp(exp(5)) + 1)^2)))/9 + (exp(exp(5))*(5832*exp(exp(5)) + 486))/(81*(12*exp(exp(5))
+ 1)^2) + (4*exp(-exp(5))*(1944*exp(exp(5)) + 162))/(2187*(12*exp(exp(5)) + 1)^2) - (4*exp(-exp(5))*(5832*exp
(exp(5)) + 486))/(6561*(12*exp(exp(5)) + 1)^2) - (exp(-exp(5))*(88*exp(exp(5)) - 4)*(1944*exp(exp(5)) + 162))/
(2916*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*(204*exp(exp(5)) - 44)*(1944*exp(exp(5)) + 162))/(8748*(12*exp(e
xp(5)) + 1)^2) + (exp(-exp(5))*(88*exp(exp(5)) - 4)*(5832*exp(exp(5)) + 486))/(8748*(12*exp(exp(5)) + 1)^2) -
(exp(-exp(5))*(204*exp(exp(5)) - 44)*(5832*exp(exp(5)) + 486))/(26244*(12*exp(exp(5)) + 1)^2) + (exp(-exp(5))*
(1944*exp(exp(5)) + 162)*(36*exp(2*exp(5)) + 8*exp(exp(5)) + 6*exp(exp(5))*(4*exp(exp(5)) - 2/3)))/(972*(12*ex
p(exp(5)) + 1)^2) - (exp(-exp(5))*(5832*exp(exp(5)) + 486)*(36*exp(2*exp(5)) + 8*exp(exp(5)) + 6*exp(exp(5))*(
4*exp(exp(5)) - 2/3)))/(2916*(12*exp(exp(5)) + 1)^2)) + (exp(2*exp(5))*(1944*exp(exp(5)) + 162))/(81*(12*exp(e
xp(5)) + 1)^2))/(x - exp(exp(5)) + 3*x^2) - (x*((x^2)^(1/4) - 4) + (x*log(x/(exp(2*exp(5)) + exp(exp(5))*(2*x
+ 2*x^2) + x^2 + 2*x^3 + x^4))*(3*(x^2)^(1/4) - 8)*(x + exp(exp(5)) + x^2))/(2*(x - exp(exp(5)) + 3*x^2)))/log
(x/(exp(2*exp(5)) + exp(exp(5))*(2*x + 2*x^2) + x^2 + 2*x^3 + x^4)) - (4*x)/3

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sympy [B]  time = 22.54, size = 95, normalized size = 3.17 \begin {gather*} - \frac {x \sqrt [4]{x^{2}}}{\log {\relax (x )} - \log {\left (x^{4} + 2 x^{3} + x^{2} + 2 x^{2} e^{e^{5}} + 2 x e^{e^{5}} + e^{2 e^{5}} \right )}} + \frac {4 x}{\log {\relax (x )} - \log {\left (x^{4} + 2 x^{3} + x^{2} + 2 x^{2} e^{e^{5}} + 2 x e^{e^{5}} + e^{2 e^{5}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-3*exp(exp(5))-3*x**2-3*x)*(x**2)**(1/4)+8*exp(exp(5))+8*x**2+8*x)*ln(x/(exp(exp(5))**2+(2*x**2+2
*x)*exp(exp(5))+x**4+2*x**3+x**2))+(2*exp(exp(5))-6*x**2-2*x)*(x**2)**(1/4)-8*exp(exp(5))+24*x**2+8*x)/(2*exp(
exp(5))+2*x**2+2*x)/ln(x/(exp(exp(5))**2+(2*x**2+2*x)*exp(exp(5))+x**4+2*x**3+x**2))**2,x)

[Out]

-x*(x**2)**(1/4)/(log(x) - log(x**4 + 2*x**3 + x**2 + 2*x**2*exp(exp(5)) + 2*x*exp(exp(5)) + exp(2*exp(5)))) +
4*x/(log(x) - log(x**4 + 2*x**3 + x**2 + 2*x**2*exp(exp(5)) + 2*x*exp(exp(5)) + exp(2*exp(5))))

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