3.47.84 \(\int \frac {-2 x^3+2 x^2 \log ^2(2)+(-5 x^2-6 x^3-x^4+(5 x^2+x^3) \log ^2(2)) \log (\frac {3}{5+x})+(10 x^2+2 x^3+(-10 x-2 x^2) \log ^2(2)) \log (\frac {3}{5+x}) \log (-x+\log ^2(2))+(-10 x^2-2 x^3+(10 x+2 x^2) \log ^2(2)) \log (\frac {3}{5+x}) \log (\log ^2(\frac {3}{5+x}))}{(-5 x^3-x^4+(5 x^2+x^3) \log ^2(2)) \log (\frac {3}{5+x})+(10 x^2+2 x^3+(-10 x-2 x^2) \log ^2(2)) \log (\frac {3}{5+x}) \log (-x+\log ^2(2))+(-5 x-x^2+(5+x) \log ^2(2)) \log (\frac {3}{5+x}) \log ^2(-x+\log ^2(2))+((-10 x^2-2 x^3+(10 x+2 x^2) \log ^2(2)) \log (\frac {3}{5+x})+(10 x+2 x^2+(-10-2 x) \log ^2(2)) \log (\frac {3}{5+x}) \log (-x+\log ^2(2))) \log (\log ^2(\frac {3}{5+x}))+(-5 x-x^2+(5+x) \log ^2(2)) \log (\frac {3}{5+x}) \log ^2(\log ^2(\frac {3}{5+x}))} \, dx\)

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

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Rubi [F]  time = 13.08, 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 {-2 x^3+2 x^2 \log ^2(2)+\left (-5 x^2-6 x^3-x^4+\left (5 x^2+x^3\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )+\left (10 x^2+2 x^3+\left (-10 x-2 x^2\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log \left (-x+\log ^2(2)\right )+\left (-10 x^2-2 x^3+\left (10 x+2 x^2\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log \left (\log ^2\left (\frac {3}{5+x}\right )\right )}{\left (-5 x^3-x^4+\left (5 x^2+x^3\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )+\left (10 x^2+2 x^3+\left (-10 x-2 x^2\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log \left (-x+\log ^2(2)\right )+\left (-5 x-x^2+(5+x) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (\left (-10 x^2-2 x^3+\left (10 x+2 x^2\right ) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )+\left (10 x+2 x^2+(-10-2 x) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log \left (-x+\log ^2(2)\right )\right ) \log \left (\log ^2\left (\frac {3}{5+x}\right )\right )+\left (-5 x-x^2+(5+x) \log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \log ^2\left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^3 + 2*x^2*Log[2]^2 + (-5*x^2 - 6*x^3 - x^4 + (5*x^2 + x^3)*Log[2]^2)*Log[3/(5 + x)] + (10*x^2 + 2*x^
3 + (-10*x - 2*x^2)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2] + (-10*x^2 - 2*x^3 + (10*x + 2*x^2)*Log[2]^2)*
Log[3/(5 + x)]*Log[Log[3/(5 + x)]^2])/((-5*x^3 - x^4 + (5*x^2 + x^3)*Log[2]^2)*Log[3/(5 + x)] + (10*x^2 + 2*x^
3 + (-10*x - 2*x^2)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2] + (-5*x - x^2 + (5 + x)*Log[2]^2)*Log[3/(5 + x
)]*Log[-x + Log[2]^2]^2 + ((-10*x^2 - 2*x^3 + (10*x + 2*x^2)*Log[2]^2)*Log[3/(5 + x)] + (10*x + 2*x^2 + (-10 -
2*x)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2])*Log[Log[3/(5 + x)]^2] + (-5*x - x^2 + (5 + x)*Log[2]^2)*Log
[3/(5 + x)]*Log[Log[3/(5 + x)]^2]^2),x]

[Out]

5*(1 + Log[2]^2)*Defer[Int][(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^(-2), x] - (125*Defer[Int][(x - L
og[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^(-2), x])/(5 + Log[2]^2) - (Log[2]^6*Defer[Int][(x - Log[-x + Log[2
]^2] + Log[Log[3/(5 + x)]^2])^(-2), x])/(5 + Log[2]^2) + (25*(4 - Log[2]^2)*Defer[Int][(x - Log[-x + Log[2]^2]
+ Log[Log[3/(5 + x)]^2])^(-2), x])/(5 + Log[2]^2) - (Log[2]^4*(4 - Log[2]^2)*Defer[Int][(x - Log[-x + Log[2]^
2] + Log[Log[3/(5 + x)]^2])^(-2), x])/(5 + Log[2]^2) - (4 - Log[2]^2)*Defer[Int][x/(x - Log[-x + Log[2]^2] + L
og[Log[3/(5 + x)]^2])^2, x] + (25*Defer[Int][x/(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2, x])/(5 + Lo
g[2]^2) - (Log[2]^4*Defer[Int][x/(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2, x])/(5 + Log[2]^2) - Defe
r[Int][x^2/(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2, x] + (625*Defer[Int][1/((5 + x)*(x - Log[-x + L
og[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) - (125*(4 - Log[2]^2)*Defer[Int][1/((5 + x)*(x - Log[
-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) - (125*(1 + Log[2]^2)*Defer[Int][1/((5 + x)*(x
- Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + (5*Log[2]^4*(1 + Log[2]^2)*Defer[Int][1
/((x - Log[2]^2)*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + (Log[2]^8*Defer[Int
][1/((-x + Log[2]^2)*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + (Log[2]^6*(4 -
Log[2]^2)*Defer[Int][1/((-x + Log[2]^2)*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2
) - 2*Log[2]^2*Defer[Int][1/(Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x] - (50*Defe
r[Int][1/(Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + (2*Log[2]^4
*Defer[Int][1/(Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + 2*Defe
r[Int][x/(Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x] + (250*Defer[Int][1/((5 + x)*
Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + (50*Log[2]^2*Defer[In
t][1/((5 + x)*Log[3/(5 + x)]*(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])^2), x])/(5 + Log[2]^2) + 2*Defer
[Int][x/(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (2 x \left (x-\log ^2(2)\right )+(5+x) \log \left (\frac {3}{5+x}\right ) \left (x \left (1+x-\log ^2(2)\right )-2 \left (x-\log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+2 \left (x-\log ^2(2)\right ) \log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )\right )}{(5+x) \left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx\\ &=\int \left (\frac {x^2 \left (2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )\right )}{(5+x) \left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2}+\frac {2 x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )}\right ) \, dx\\ &=2 \int \frac {x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx+\int \frac {x^2 \left (2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )\right )}{(5+x) \left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx\\ &=2 \int \frac {x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx+\int \frac {x^2 \left (2 x-2 \log ^2(2)-(5+x) \left (-1+x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )\right )}{(5+x) \left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx\\ &=2 \int \frac {x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx+\int \left (\frac {25 \left (-2 x+2 \log ^2(2)+x^2 \log \left (\frac {3}{5+x}\right )+4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )-5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )\right )}{(5+x) \left (5+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2}+\frac {2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{\log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2}+\frac {\log ^4(2) \left (2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )\right )}{\left (x-\log ^2(2)\right ) \left (5+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx+\frac {25 \int \frac {-2 x+2 \log ^2(2)+x^2 \log \left (\frac {3}{5+x}\right )+4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )-5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{(5+x) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx}{5+\log ^2(2)}+\frac {\log ^4(2) \int \frac {2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{\left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx}{5+\log ^2(2)}+\int \frac {2 x-2 \log ^2(2)-x^2 \log \left (\frac {3}{5+x}\right )-4 x \left (1-\frac {\log ^2(2)}{4}\right ) \log \left (\frac {3}{5+x}\right )+5 \left (1+\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{\log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx\\ &=2 \int \frac {x}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \, dx+\frac {25 \int \frac {-2 x+2 \log ^2(2)+(5+x) \left (-1+x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{(5+x) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx}{5+\log ^2(2)}+\frac {\log ^4(2) \int \frac {2 \left (x-\log ^2(2)\right )-(5+x) \left (-1+x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{\left (x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx}{5+\log ^2(2)}+\int \frac {2 \left (x-\log ^2(2)\right )-(5+x) \left (-1+x-\log ^2(2)\right ) \log \left (\frac {3}{5+x}\right )}{\log \left (\frac {3}{5+x}\right ) \left (x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.13, size = 30, normalized size = 1.00 \begin {gather*} \frac {x^2}{x-\log \left (-x+\log ^2(2)\right )+\log \left (\log ^2\left (\frac {3}{5+x}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^3 + 2*x^2*Log[2]^2 + (-5*x^2 - 6*x^3 - x^4 + (5*x^2 + x^3)*Log[2]^2)*Log[3/(5 + x)] + (10*x^2
+ 2*x^3 + (-10*x - 2*x^2)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2] + (-10*x^2 - 2*x^3 + (10*x + 2*x^2)*Log[
2]^2)*Log[3/(5 + x)]*Log[Log[3/(5 + x)]^2])/((-5*x^3 - x^4 + (5*x^2 + x^3)*Log[2]^2)*Log[3/(5 + x)] + (10*x^2
+ 2*x^3 + (-10*x - 2*x^2)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2] + (-5*x - x^2 + (5 + x)*Log[2]^2)*Log[3/
(5 + x)]*Log[-x + Log[2]^2]^2 + ((-10*x^2 - 2*x^3 + (10*x + 2*x^2)*Log[2]^2)*Log[3/(5 + x)] + (10*x + 2*x^2 +
(-10 - 2*x)*Log[2]^2)*Log[3/(5 + x)]*Log[-x + Log[2]^2])*Log[Log[3/(5 + x)]^2] + (-5*x - x^2 + (5 + x)*Log[2]^
2)*Log[3/(5 + x)]*Log[Log[3/(5 + x)]^2]^2),x]

[Out]

x^2/(x - Log[-x + Log[2]^2] + Log[Log[3/(5 + x)]^2])

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fricas [A]  time = 0.75, size = 30, normalized size = 1.00 \begin {gather*} \frac {x^{2}}{x - \log \left (\log \relax (2)^{2} - x\right ) + \log \left (\log \left (\frac {3}{x + 5}\right )^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x))*log(log(3/(5+x))^2)+((-2*x^2-10*x)*log(2)^2+2*x^3
+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2)*log(2)^2-x^4-6*x^3-5*x^2)*log(3/(5+x))+2*x^2*log(2)^2-2*x^3
)/(((5+x)*log(2)^2-x^2-5*x)*log(3/(5+x))*log(log(3/(5+x))^2)^2+(((-2*x-10)*log(2)^2+2*x^2+10*x)*log(3/(5+x))*l
og(log(2)^2-x)+((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x)))*log(log(3/(5+x))^2)+((5+x)*log(2)^2-x^2-5*x)
*log(3/(5+x))*log(log(2)^2-x)^2+((-2*x^2-10*x)*log(2)^2+2*x^3+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2
)*log(2)^2-x^4-5*x^3)*log(3/(5+x))),x, algorithm="fricas")

[Out]

x^2/(x - log(log(2)^2 - x) + log(log(3/(x + 5))^2))

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giac [B]  time = 59.41, size = 1059, normalized size = 35.30 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x))*log(log(3/(5+x))^2)+((-2*x^2-10*x)*log(2)^2+2*x^3
+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2)*log(2)^2-x^4-6*x^3-5*x^2)*log(3/(5+x))+2*x^2*log(2)^2-2*x^3
)/(((5+x)*log(2)^2-x^2-5*x)*log(3/(5+x))*log(log(3/(5+x))^2)^2+(((-2*x-10)*log(2)^2+2*x^2+10*x)*log(3/(5+x))*l
og(log(2)^2-x)+((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x)))*log(log(3/(5+x))^2)+((5+x)*log(2)^2-x^2-5*x)
*log(3/(5+x))*log(log(2)^2-x)^2+((-2*x^2-10*x)*log(2)^2+2*x^3+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2
)*log(2)^2-x^4-5*x^3)*log(3/(5+x))),x, algorithm="giac")

[Out]

(x^3*log(3)*log(2)^2*log(3/(x + 5)) - x^3*log(2)^2*log(x + 5)*log(3/(x + 5)) - x^4*log(3)*log(3/(x + 5)) + 5*x
^2*log(3)*log(2)^2*log(3/(x + 5)) + x^4*log(x + 5)*log(3/(x + 5)) - 5*x^2*log(2)^2*log(x + 5)*log(3/(x + 5)) -
4*x^3*log(3)*log(3/(x + 5)) - 2*x^2*log(2)^2*log(3/(x + 5)) + 4*x^3*log(x + 5)*log(3/(x + 5)) + 2*x^3*log(3/(
x + 5)) + 5*x^2*log(3)*log(3/(x + 5)) - 5*x^2*log(x + 5)*log(3/(x + 5)))/(x^2*log(3)*log(2)^2*log(3/(x + 5)) -
x*log(3)*log(2)^2*log(log(2)^2 - x)*log(3/(x + 5)) + x*log(3)*log(2)^2*log(log(3/(x + 5))^2)*log(3/(x + 5)) -
x^2*log(2)^2*log(x + 5)*log(3/(x + 5)) + x*log(2)^2*log(log(2)^2 - x)*log(x + 5)*log(3/(x + 5)) - x*log(2)^2*
log(log(3/(x + 5))^2)*log(x + 5)*log(3/(x + 5)) - x^3*log(3)*log(3/(x + 5)) + 5*x*log(3)*log(2)^2*log(3/(x + 5
)) + x^2*log(3)*log(log(2)^2 - x)*log(3/(x + 5)) - 5*log(3)*log(2)^2*log(log(2)^2 - x)*log(3/(x + 5)) - x^2*lo
g(3)*log(log(3/(x + 5))^2)*log(3/(x + 5)) + 5*log(3)*log(2)^2*log(log(3/(x + 5))^2)*log(3/(x + 5)) + x^3*log(x
+ 5)*log(3/(x + 5)) - 5*x*log(2)^2*log(x + 5)*log(3/(x + 5)) - x^2*log(log(2)^2 - x)*log(x + 5)*log(3/(x + 5)
) + 5*log(2)^2*log(log(2)^2 - x)*log(x + 5)*log(3/(x + 5)) + x^2*log(log(3/(x + 5))^2)*log(x + 5)*log(3/(x + 5
)) - 5*log(2)^2*log(log(3/(x + 5))^2)*log(x + 5)*log(3/(x + 5)) - 2*x*log(3)*log(2)^2 + 2*log(3)*log(2)^2*log(
log(2)^2 - x) - 2*log(3)*log(2)^2*log(log(3/(x + 5))^2) + 2*x*log(2)^2*log(x + 5) - 2*log(2)^2*log(log(2)^2 -
x)*log(x + 5) + 2*log(2)^2*log(log(3/(x + 5))^2)*log(x + 5) - 4*x^2*log(3)*log(3/(x + 5)) + 4*x*log(3)*log(log
(2)^2 - x)*log(3/(x + 5)) - 4*x*log(3)*log(log(3/(x + 5))^2)*log(3/(x + 5)) + 4*x^2*log(x + 5)*log(3/(x + 5))
- 4*x*log(log(2)^2 - x)*log(x + 5)*log(3/(x + 5)) + 4*x*log(log(3/(x + 5))^2)*log(x + 5)*log(3/(x + 5)) + 2*x^
2*log(3) - 2*x*log(3)*log(log(2)^2 - x) + 2*x*log(3)*log(log(3/(x + 5))^2) - 2*x^2*log(x + 5) + 2*x*log(log(2)
^2 - x)*log(x + 5) - 2*x*log(log(3/(x + 5))^2)*log(x + 5) + 5*x*log(3)*log(3/(x + 5)) - 5*log(3)*log(log(2)^2
- x)*log(3/(x + 5)) + 5*log(3)*log(log(3/(x + 5))^2)*log(3/(x + 5)) - 5*x*log(x + 5)*log(3/(x + 5)) + 5*log(lo
g(2)^2 - x)*log(x + 5)*log(3/(x + 5)) - 5*log(log(3/(x + 5))^2)*log(x + 5)*log(3/(x + 5)))

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maple [C]  time = 0.90, size = 181, normalized size = 6.03

method	result	size
risch	\(\frac {2 x^{2}}{-2 i \pi \mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )\right )^{2} \mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )\right ) \mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )^{2}\right )^{2}+i \pi \mathrm {csgn}\left (i \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )^{2}\right )^{3}+2 i \pi -4 \ln \relax (2)+2 x -2 \ln \left (\ln \relax (2)^{2}-x \right )+4 \ln \left (-2 i \ln \left (5+x \right )+2 i \ln \relax (3)\right )}\)	\(181\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2+10*x)*ln(2)^2-2*x^3-10*x^2)*ln(3/(5+x))*ln(ln(3/(5+x))^2)+((-2*x^2-10*x)*ln(2)^2+2*x^3+10*x^2)*ln
(3/(5+x))*ln(ln(2)^2-x)+((x^3+5*x^2)*ln(2)^2-x^4-6*x^3-5*x^2)*ln(3/(5+x))+2*x^2*ln(2)^2-2*x^3)/(((5+x)*ln(2)^2
-x^2-5*x)*ln(3/(5+x))*ln(ln(3/(5+x))^2)^2+(((-2*x-10)*ln(2)^2+2*x^2+10*x)*ln(3/(5+x))*ln(ln(2)^2-x)+((2*x^2+10
*x)*ln(2)^2-2*x^3-10*x^2)*ln(3/(5+x)))*ln(ln(3/(5+x))^2)+((5+x)*ln(2)^2-x^2-5*x)*ln(3/(5+x))*ln(ln(2)^2-x)^2+(
(-2*x^2-10*x)*ln(2)^2+2*x^3+10*x^2)*ln(3/(5+x))*ln(ln(2)^2-x)+((x^3+5*x^2)*ln(2)^2-x^4-5*x^3)*ln(3/(5+x))),x,m
ethod=_RETURNVERBOSE)

[Out]

2*x^2/(-2*I*Pi*csgn(I*(-2*I*ln(5+x)+2*I*ln(3))^2)^2-I*Pi*csgn(I*(-2*I*ln(5+x)+2*I*ln(3)))^2*csgn(I*(-2*I*ln(5+
x)+2*I*ln(3))^2)+2*I*Pi*csgn(I*(-2*I*ln(5+x)+2*I*ln(3)))*csgn(I*(-2*I*ln(5+x)+2*I*ln(3))^2)^2+I*Pi*csgn(I*(-2*
I*ln(5+x)+2*I*ln(3))^2)^3+2*I*Pi-4*ln(2)+2*x-2*ln(ln(2)^2-x)+4*ln(-2*I*ln(5+x)+2*I*ln(3)))

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maxima [A]  time = 0.64, size = 31, normalized size = 1.03 \begin {gather*} \frac {x^{2}}{x - \log \left (\log \relax (2)^{2} - x\right ) + 2 \, \log \left (-\log \relax (3) + \log \left (x + 5\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x))*log(log(3/(5+x))^2)+((-2*x^2-10*x)*log(2)^2+2*x^3
+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2)*log(2)^2-x^4-6*x^3-5*x^2)*log(3/(5+x))+2*x^2*log(2)^2-2*x^3
)/(((5+x)*log(2)^2-x^2-5*x)*log(3/(5+x))*log(log(3/(5+x))^2)^2+(((-2*x-10)*log(2)^2+2*x^2+10*x)*log(3/(5+x))*l
og(log(2)^2-x)+((2*x^2+10*x)*log(2)^2-2*x^3-10*x^2)*log(3/(5+x)))*log(log(3/(5+x))^2)+((5+x)*log(2)^2-x^2-5*x)
*log(3/(5+x))*log(log(2)^2-x)^2+((-2*x^2-10*x)*log(2)^2+2*x^3+10*x^2)*log(3/(5+x))*log(log(2)^2-x)+((x^3+5*x^2
)*log(2)^2-x^4-5*x^3)*log(3/(5+x))),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (\frac {3}{x+5}\right )\,\left (5\,x^2-{\ln \relax (2)}^2\,\left (x^3+5\,x^2\right )+6\,x^3+x^4\right )-2\,x^2\,{\ln \relax (2)}^2+2\,x^3-\ln \left (\frac {3}{x+5}\right )\,\ln \left ({\ln \relax (2)}^2-x\right )\,\left (10\,x^2-{\ln \relax (2)}^2\,\left (2\,x^2+10\,x\right )+2\,x^3\right )+\ln \left (\frac {3}{x+5}\right )\,\ln \left ({\ln \left (\frac {3}{x+5}\right )}^2\right )\,\left (10\,x^2-{\ln \relax (2)}^2\,\left (2\,x^2+10\,x\right )+2\,x^3\right )}{\ln \left (\frac {3}{x+5}\right )\,\left (5\,x^3-{\ln \relax (2)}^2\,\left (x^3+5\,x^2\right )+x^4\right )+\ln \left ({\ln \left (\frac {3}{x+5}\right )}^2\right )\,\left (\ln \left (\frac {3}{x+5}\right )\,\left (10\,x^2-{\ln \relax (2)}^2\,\left (2\,x^2+10\,x\right )+2\,x^3\right )-\ln \left (\frac {3}{x+5}\right )\,\ln \left ({\ln \relax (2)}^2-x\right )\,\left (10\,x-{\ln \relax (2)}^2\,\left (2\,x+10\right )+2\,x^2\right )\right )-\ln \left (\frac {3}{x+5}\right )\,\ln \left ({\ln \relax (2)}^2-x\right )\,\left (10\,x^2-{\ln \relax (2)}^2\,\left (2\,x^2+10\,x\right )+2\,x^3\right )+\ln \left (\frac {3}{x+5}\right )\,{\ln \left ({\ln \relax (2)}^2-x\right )}^2\,\left (5\,x-{\ln \relax (2)}^2\,\left (x+5\right )+x^2\right )+\ln \left (\frac {3}{x+5}\right )\,{\ln \left ({\ln \left (\frac {3}{x+5}\right )}^2\right )}^2\,\left (5\,x-{\ln \relax (2)}^2\,\left (x+5\right )+x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(3/(x + 5))*(5*x^2 - log(2)^2*(5*x^2 + x^3) + 6*x^3 + x^4) - 2*x^2*log(2)^2 + 2*x^3 - log(3/(x + 5))*l
og(log(2)^2 - x)*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) + log(3/(x + 5))*log(log(3/(x + 5))^2)*(10*x^2 - l
og(2)^2*(10*x + 2*x^2) + 2*x^3))/(log(3/(x + 5))*(5*x^3 - log(2)^2*(5*x^2 + x^3) + x^4) + log(log(3/(x + 5))^2
)*(log(3/(x + 5))*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) - log(3/(x + 5))*log(log(2)^2 - x)*(10*x - log(2)
^2*(2*x + 10) + 2*x^2)) - log(3/(x + 5))*log(log(2)^2 - x)*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) + log(3/
(x + 5))*log(log(2)^2 - x)^2*(5*x - log(2)^2*(x + 5) + x^2) + log(3/(x + 5))*log(log(3/(x + 5))^2)^2*(5*x - lo
g(2)^2*(x + 5) + x^2)),x)

[Out]

int((log(3/(x + 5))*(5*x^2 - log(2)^2*(5*x^2 + x^3) + 6*x^3 + x^4) - 2*x^2*log(2)^2 + 2*x^3 - log(3/(x + 5))*l
og(log(2)^2 - x)*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) + log(3/(x + 5))*log(log(3/(x + 5))^2)*(10*x^2 - l
og(2)^2*(10*x + 2*x^2) + 2*x^3))/(log(3/(x + 5))*(5*x^3 - log(2)^2*(5*x^2 + x^3) + x^4) + log(log(3/(x + 5))^2
)*(log(3/(x + 5))*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) - log(3/(x + 5))*log(log(2)^2 - x)*(10*x - log(2)
^2*(2*x + 10) + 2*x^2)) - log(3/(x + 5))*log(log(2)^2 - x)*(10*x^2 - log(2)^2*(10*x + 2*x^2) + 2*x^3) + log(3/
(x + 5))*log(log(2)^2 - x)^2*(5*x - log(2)^2*(x + 5) + x^2) + log(3/(x + 5))*log(log(3/(x + 5))^2)^2*(5*x - lo
g(2)^2*(x + 5) + x^2)), x)

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sympy [A]  time = 0.89, size = 22, normalized size = 0.73 \begin {gather*} \frac {x^{2}}{x - \log {\left (- x + \log {\relax (2 )}^{2} \right )} + \log {\left (\log {\left (\frac {3}{x + 5} \right )}^{2} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2+10*x)*ln(2)**2-2*x**3-10*x**2)*ln(3/(5+x))*ln(ln(3/(5+x))**2)+((-2*x**2-10*x)*ln(2)**2+2*x
**3+10*x**2)*ln(3/(5+x))*ln(ln(2)**2-x)+((x**3+5*x**2)*ln(2)**2-x**4-6*x**3-5*x**2)*ln(3/(5+x))+2*x**2*ln(2)**
2-2*x**3)/(((5+x)*ln(2)**2-x**2-5*x)*ln(3/(5+x))*ln(ln(3/(5+x))**2)**2+(((-2*x-10)*ln(2)**2+2*x**2+10*x)*ln(3/
(5+x))*ln(ln(2)**2-x)+((2*x**2+10*x)*ln(2)**2-2*x**3-10*x**2)*ln(3/(5+x)))*ln(ln(3/(5+x))**2)+((5+x)*ln(2)**2-
x**2-5*x)*ln(3/(5+x))*ln(ln(2)**2-x)**2+((-2*x**2-10*x)*ln(2)**2+2*x**3+10*x**2)*ln(3/(5+x))*ln(ln(2)**2-x)+((
x**3+5*x**2)*ln(2)**2-x**4-5*x**3)*ln(3/(5+x))),x)

[Out]

x**2/(x - log(-x + log(2)**2) + log(log(3/(x + 5))**2))

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