3.44.89 \(\int \frac {-5 x-x^2-6 x^3+10 x^4-4 x^5+(-10+2 x) \log (2 x)+(-2 x-12 x^2+20 x^3-8 x^4) \log ^2(2 x)+(-6 x+10 x^2-4 x^3) \log ^4(2 x)+(-x^2-3 x^3-x^5+(-x-6 x^2-2 x^4) \log ^2(2 x)+(-3 x-x^3) \log ^4(2 x)) \log (\frac {1+3 x+x^3+(3+x^2) \log ^2(2 x)}{x+\log ^2(2 x)})}{x^2+3 x^3+x^5+(x+6 x^2+2 x^4) \log ^2(2 x)+(3 x+x^3) \log ^4(2 x)} \, dx\)

Optimal. Leaf size=26 \[ 2+(5-x) \left (2+\log \left (3+x^2+\frac {1}{x+\log ^2(2 x)}\right )\right ) \]

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Rubi [F]  time = 33.50, 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 {-5 x-x^2-6 x^3+10 x^4-4 x^5+(-10+2 x) \log (2 x)+\left (-2 x-12 x^2+20 x^3-8 x^4\right ) \log ^2(2 x)+\left (-6 x+10 x^2-4 x^3\right ) \log ^4(2 x)+\left (-x^2-3 x^3-x^5+\left (-x-6 x^2-2 x^4\right ) \log ^2(2 x)+\left (-3 x-x^3\right ) \log ^4(2 x)\right ) \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )}{x^2+3 x^3+x^5+\left (x+6 x^2+2 x^4\right ) \log ^2(2 x)+\left (3 x+x^3\right ) \log ^4(2 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-5*x - x^2 - 6*x^3 + 10*x^4 - 4*x^5 + (-10 + 2*x)*Log[2*x] + (-2*x - 12*x^2 + 20*x^3 - 8*x^4)*Log[2*x]^2
+ (-6*x + 10*x^2 - 4*x^3)*Log[2*x]^4 + (-x^2 - 3*x^3 - x^5 + (-x - 6*x^2 - 2*x^4)*Log[2*x]^2 + (-3*x - x^3)*Lo
g[2*x]^4)*Log[(1 + 3*x + x^3 + (3 + x^2)*Log[2*x]^2)/(x + Log[2*x]^2)])/(x^2 + 3*x^3 + x^5 + (x + 6*x^2 + 2*x^
4)*Log[2*x]^2 + (3*x + x^3)*Log[2*x]^4),x]

[Out]

-2*x + 5*Log[3 + x^2] - 5*Log[x + Log[2*x]^2] - x*Log[(1 + 3*x + x^3 + (3 + x^2)*Log[2*x]^2)/(x + Log[2*x]^2)]
+ 15*Defer[Int][(1 + 3*x + x^3 + 3*Log[2*x]^2 + x^2*Log[2*x]^2)^(-1), x] + 5*Defer[Int][1/((I*Sqrt[3] - x)*(1
+ 3*x + x^3 + 3*Log[2*x]^2 + x^2*Log[2*x]^2)), x] + 5*Defer[Int][x^2/(1 + 3*x + x^3 + 3*Log[2*x]^2 + x^2*Log[
2*x]^2), x] - 5*Defer[Int][1/((I*Sqrt[3] + x)*(1 + 3*x + x^3 + 3*Log[2*x]^2 + x^2*Log[2*x]^2)), x] + 30*Defer[
Int][Log[2*x]/(x*(1 + 3*x + x^3 + 3*Log[2*x]^2 + x^2*Log[2*x]^2)), x] + 10*Defer[Int][(x*Log[2*x])/(1 + 3*x +
x^3 + 3*Log[2*x]^2 + x^2*Log[2*x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {5}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\frac {x}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\frac {6 x^2}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}+\frac {10 x^3}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\frac {4 x^4}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}+\frac {2 (-5+x) \log (2 x)}{x \left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\frac {2 \left (1+6 x-10 x^2+4 x^3\right ) \log ^2(2 x)}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\frac {2 (-1+x) (-3+2 x) \log ^4(2 x)}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}-\log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )\right ) \, dx\\ &=2 \int \frac {(-5+x) \log (2 x)}{x \left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-2 \int \frac {\left (1+6 x-10 x^2+4 x^3\right ) \log ^2(2 x)}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-2 \int \frac {(-1+x) (-3+2 x) \log ^4(2 x)}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-4 \int \frac {x^4}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-5 \int \frac {1}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-6 \int \frac {x^2}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx+10 \int \frac {x^3}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-\int \frac {x}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-\int \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right ) \, dx\\ &=-x \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )-2 \int \left (\frac {3-5 x+2 x^2}{3+x^2}+\frac {x^2 \left (3-5 x+2 x^2\right )}{x+\log ^2(2 x)}-\frac {\left (3-5 x+2 x^2\right ) \left (1+3 x+x^3\right )^2}{\left (3+x^2\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}\right ) \, dx-2 \int \left (-\frac {x \left (1+6 x-10 x^2+4 x^3\right )}{x+\log ^2(2 x)}+\frac {\left (1+3 x+x^3\right ) \left (1+6 x-10 x^2+4 x^3\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx+2 \int \left (\frac {(-5+x) \log (2 x)}{x \left (x+\log ^2(2 x)\right )}-\frac {(-5+x) \left (3+x^2\right ) \log (2 x)}{x \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}\right ) \, dx-4 \int \left (\frac {x^4}{x+\log ^2(2 x)}-\frac {x^4 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx-5 \int \left (\frac {1}{x+\log ^2(2 x)}+\frac {-3-x^2}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx-6 \int \left (\frac {x^2}{x+\log ^2(2 x)}-\frac {x^2 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx+10 \int \left (\frac {x^3}{x+\log ^2(2 x)}-\frac {x^3 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx+\int \frac {-x+2 x^4-2 \log (2 x)+4 x^3 \log ^2(2 x)+2 x^2 \log ^4(2 x)}{\left (x+\log ^2(2 x)\right ) \left (1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)\right )} \, dx-\int \left (\frac {x}{x+\log ^2(2 x)}-\frac {x \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)}\right ) \, dx\\ &=-x \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right )-2 \int \frac {3-5 x+2 x^2}{3+x^2} \, dx-2 \int \frac {x^2 \left (3-5 x+2 x^2\right )}{x+\log ^2(2 x)} \, dx+2 \int \frac {x \left (1+6 x-10 x^2+4 x^3\right )}{x+\log ^2(2 x)} \, dx+2 \int \frac {(-5+x) \log (2 x)}{x \left (x+\log ^2(2 x)\right )} \, dx+2 \int \frac {\left (3-5 x+2 x^2\right ) \left (1+3 x+x^3\right )^2}{\left (3+x^2\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-2 \int \frac {\left (1+3 x+x^3\right ) \left (1+6 x-10 x^2+4 x^3\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx-2 \int \frac {(-5+x) \left (3+x^2\right ) \log (2 x)}{x \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )} \, dx-4 \int \frac {x^4}{x+\log ^2(2 x)} \, dx+4 \int \frac {x^4 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx-5 \int \frac {1}{x+\log ^2(2 x)} \, dx-5 \int \frac {-3-x^2}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx-6 \int \frac {x^2}{x+\log ^2(2 x)} \, dx+6 \int \frac {x^2 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx+10 \int \frac {x^3}{x+\log ^2(2 x)} \, dx-10 \int \frac {x^3 \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx-\int \frac {x}{x+\log ^2(2 x)} \, dx+\int \frac {x \left (3+x^2\right )}{1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)} \, dx+\int \left (\frac {2 x^2}{3+x^2}+\frac {-x-2 \log (2 x)}{x+\log ^2(2 x)}+\frac {9 x-2 x^2+6 x^3+x^5+18 \log (2 x)+12 x^2 \log (2 x)+2 x^4 \log (2 x)}{\left (3+x^2\right ) \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.69, size = 79, normalized size = 3.04 \begin {gather*} -2 x-5 \log \left (x+\log ^2(2 x)\right )+5 \log \left (1+3 x+x^3+3 \log ^2(2 x)+x^2 \log ^2(2 x)\right )-x \log \left (\frac {1+3 x+x^3+\left (3+x^2\right ) \log ^2(2 x)}{x+\log ^2(2 x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-5*x - x^2 - 6*x^3 + 10*x^4 - 4*x^5 + (-10 + 2*x)*Log[2*x] + (-2*x - 12*x^2 + 20*x^3 - 8*x^4)*Log[2
*x]^2 + (-6*x + 10*x^2 - 4*x^3)*Log[2*x]^4 + (-x^2 - 3*x^3 - x^5 + (-x - 6*x^2 - 2*x^4)*Log[2*x]^2 + (-3*x - x
^3)*Log[2*x]^4)*Log[(1 + 3*x + x^3 + (3 + x^2)*Log[2*x]^2)/(x + Log[2*x]^2)])/(x^2 + 3*x^3 + x^5 + (x + 6*x^2
+ 2*x^4)*Log[2*x]^2 + (3*x + x^3)*Log[2*x]^4),x]

[Out]

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

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fricas [A]  time = 0.53, size = 41, normalized size = 1.58 \begin {gather*} -{\left (x - 5\right )} \log \left (\frac {x^{3} + {\left (x^{2} + 3\right )} \log \left (2 \, x\right )^{2} + 3 \, x + 1}{\log \left (2 \, x\right )^{2} + x}\right ) - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-3*x)*log(2*x)^4+(-2*x^4-6*x^2-x)*log(2*x)^2-x^5-3*x^3-x^2)*log(((x^2+3)*log(2*x)^2+x^3+3*x+1
)/(log(2*x)^2+x))+(-4*x^3+10*x^2-6*x)*log(2*x)^4+(-8*x^4+20*x^3-12*x^2-2*x)*log(2*x)^2+(2*x-10)*log(2*x)-4*x^5
+10*x^4-6*x^3-x^2-5*x)/((x^3+3*x)*log(2*x)^4+(2*x^4+6*x^2+x)*log(2*x)^2+x^5+3*x^3+x^2),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 3.00, size = 85, normalized size = 3.27 \begin {gather*} -x \log \left (x^{2} \log \left (2 \, x\right )^{2} + x^{3} + 3 \, \log \left (2 \, x\right )^{2} + 3 \, x + 1\right ) + x \log \left (\log \left (2 \, x\right )^{2} + x\right ) - 2 \, x + 5 \, \log \left (x^{2} \log \left (2 \, x\right )^{2} + x^{3} + 3 \, \log \left (2 \, x\right )^{2} + 3 \, x + 1\right ) - 5 \, \log \left (\log \left (2 \, x\right )^{2} + x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-3*x)*log(2*x)^4+(-2*x^4-6*x^2-x)*log(2*x)^2-x^5-3*x^3-x^2)*log(((x^2+3)*log(2*x)^2+x^3+3*x+1
)/(log(2*x)^2+x))+(-4*x^3+10*x^2-6*x)*log(2*x)^4+(-8*x^4+20*x^3-12*x^2-2*x)*log(2*x)^2+(2*x-10)*log(2*x)-4*x^5
+10*x^4-6*x^3-x^2-5*x)/((x^3+3*x)*log(2*x)^4+(2*x^4+6*x^2+x)*log(2*x)^2+x^5+3*x^3+x^2),x, algorithm="giac")

[Out]

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

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maple [C]  time = 0.52, size = 365, normalized size = 14.04

method	result	size
risch	\(-x \ln \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )+x \ln \left (\ln \left (2 x \right )^{2}+x \right )+\frac {i \pi x \,\mathrm {csgn}\left (\frac {i}{\ln \left (2 x \right )^{2}+x}\right ) \mathrm {csgn}\left (i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )}{\ln \left (2 x \right )^{2}+x}\right )}{2}-\frac {i \pi x \,\mathrm {csgn}\left (\frac {i}{\ln \left (2 x \right )^{2}+x}\right ) \mathrm {csgn}\left (\frac {i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )}{\ln \left (2 x \right )^{2}+x}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {csgn}\left (i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )}{\ln \left (2 x \right )^{2}+x}\right )^{2}}{2}+\frac {i \pi x \mathrm {csgn}\left (\frac {i \left (x^{2} \ln \left (2 x \right )^{2}+x^{3}+3 \ln \left (2 x \right )^{2}+3 x +1\right )}{\ln \left (2 x \right )^{2}+x}\right )^{3}}{2}-2 x +5 \ln \left (x^{2}+3\right )+5 \ln \left (\ln \left (2 x \right )^{2}+\frac {x^{3}+3 x +1}{x^{2}+3}\right )-5 \ln \left (\ln \left (2 x \right )^{2}+x \right )\)	\(365\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^3-3*x)*ln(2*x)^4+(-2*x^4-6*x^2-x)*ln(2*x)^2-x^5-3*x^3-x^2)*ln(((x^2+3)*ln(2*x)^2+x^3+3*x+1)/(ln(2*x)
^2+x))+(-4*x^3+10*x^2-6*x)*ln(2*x)^4+(-8*x^4+20*x^3-12*x^2-2*x)*ln(2*x)^2+(2*x-10)*ln(2*x)-4*x^5+10*x^4-6*x^3-
x^2-5*x)/((x^3+3*x)*ln(2*x)^4+(2*x^4+6*x^2+x)*ln(2*x)^2+x^5+3*x^3+x^2),x,method=_RETURNVERBOSE)

[Out]

-x*ln(x^2*ln(2*x)^2+x^3+3*ln(2*x)^2+3*x+1)+x*ln(ln(2*x)^2+x)+1/2*I*Pi*x*csgn(I/(ln(2*x)^2+x))*csgn(I*(x^2*ln(2
*x)^2+x^3+3*ln(2*x)^2+3*x+1))*csgn(I/(ln(2*x)^2+x)*(x^2*ln(2*x)^2+x^3+3*ln(2*x)^2+3*x+1))-1/2*I*Pi*x*csgn(I/(l
n(2*x)^2+x))*csgn(I/(ln(2*x)^2+x)*(x^2*ln(2*x)^2+x^3+3*ln(2*x)^2+3*x+1))^2-1/2*I*Pi*x*csgn(I*(x^2*ln(2*x)^2+x^
3+3*ln(2*x)^2+3*x+1))*csgn(I/(ln(2*x)^2+x)*(x^2*ln(2*x)^2+x^3+3*ln(2*x)^2+3*x+1))^2+1/2*I*Pi*x*csgn(I/(ln(2*x)
^2+x)*(x^2*ln(2*x)^2+x^3+3*ln(2*x)^2+3*x+1))^3-2*x+5*ln(x^2+3)+5*ln(ln(2*x)^2+(x^3+3*x+1)/(x^2+3))-5*ln(ln(2*x
)^2+x)

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maxima [B]  time = 1.24, size = 159, normalized size = 6.12 \begin {gather*} -x \log \left (x^{2} \log \relax (2)^{2} + x^{3} + {\left (x^{2} + 3\right )} \log \relax (x)^{2} + 3 \, \log \relax (2)^{2} + 2 \, {\left (x^{2} \log \relax (2) + 3 \, \log \relax (2)\right )} \log \relax (x) + 3 \, x + 1\right ) + x \log \left (\log \relax (2)^{2} + 2 \, \log \relax (2) \log \relax (x) + \log \relax (x)^{2} + x\right ) - 2 \, x + 5 \, \log \left (x^{2} + 3\right ) - 5 \, \log \left (\log \relax (2)^{2} + 2 \, \log \relax (2) \log \relax (x) + \log \relax (x)^{2} + x\right ) + 5 \, \log \left (\frac {x^{2} \log \relax (2)^{2} + x^{3} + {\left (x^{2} + 3\right )} \log \relax (x)^{2} + 3 \, \log \relax (2)^{2} + 2 \, {\left (x^{2} \log \relax (2) + 3 \, \log \relax (2)\right )} \log \relax (x) + 3 \, x + 1}{x^{2} + 3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3-3*x)*log(2*x)^4+(-2*x^4-6*x^2-x)*log(2*x)^2-x^5-3*x^3-x^2)*log(((x^2+3)*log(2*x)^2+x^3+3*x+1
)/(log(2*x)^2+x))+(-4*x^3+10*x^2-6*x)*log(2*x)^4+(-8*x^4+20*x^3-12*x^2-2*x)*log(2*x)^2+(2*x-10)*log(2*x)-4*x^5
+10*x^4-6*x^3-x^2-5*x)/((x^3+3*x)*log(2*x)^4+(2*x^4+6*x^2+x)*log(2*x)^2+x^5+3*x^3+x^2),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {5\,x+{\ln \left (2\,x\right )}^4\,\left (4\,x^3-10\,x^2+6\,x\right )+x^2+6\,x^3-10\,x^4+4\,x^5-\ln \left (2\,x\right )\,\left (2\,x-10\right )+{\ln \left (2\,x\right )}^2\,\left (8\,x^4-20\,x^3+12\,x^2+2\,x\right )+\ln \left (\frac {3\,x+{\ln \left (2\,x\right )}^2\,\left (x^2+3\right )+x^3+1}{{\ln \left (2\,x\right )}^2+x}\right )\,\left ({\ln \left (2\,x\right )}^4\,\left (x^3+3\,x\right )+{\ln \left (2\,x\right )}^2\,\left (2\,x^4+6\,x^2+x\right )+x^2+3\,x^3+x^5\right )}{{\ln \left (2\,x\right )}^4\,\left (x^3+3\,x\right )+{\ln \left (2\,x\right )}^2\,\left (2\,x^4+6\,x^2+x\right )+x^2+3\,x^3+x^5} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(5*x + log(2*x)^4*(6*x - 10*x^2 + 4*x^3) + x^2 + 6*x^3 - 10*x^4 + 4*x^5 - log(2*x)*(2*x - 10) + log(2*x)^
2*(2*x + 12*x^2 - 20*x^3 + 8*x^4) + log((3*x + log(2*x)^2*(x^2 + 3) + x^3 + 1)/(x + log(2*x)^2))*(log(2*x)^4*(
3*x + x^3) + log(2*x)^2*(x + 6*x^2 + 2*x^4) + x^2 + 3*x^3 + x^5))/(log(2*x)^4*(3*x + x^3) + log(2*x)^2*(x + 6*
x^2 + 2*x^4) + x^2 + 3*x^3 + x^5),x)

[Out]

int(-(5*x + log(2*x)^4*(6*x - 10*x^2 + 4*x^3) + x^2 + 6*x^3 - 10*x^4 + 4*x^5 - log(2*x)*(2*x - 10) + log(2*x)^
2*(2*x + 12*x^2 - 20*x^3 + 8*x^4) + log((3*x + log(2*x)^2*(x^2 + 3) + x^3 + 1)/(x + log(2*x)^2))*(log(2*x)^4*(
3*x + x^3) + log(2*x)^2*(x + 6*x^2 + 2*x^4) + x^2 + 3*x^3 + x^5))/(log(2*x)^4*(3*x + x^3) + log(2*x)^2*(x + 6*
x^2 + 2*x^4) + x^2 + 3*x^3 + x^5), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**3-3*x)*ln(2*x)**4+(-2*x**4-6*x**2-x)*ln(2*x)**2-x**5-3*x**3-x**2)*ln(((x**2+3)*ln(2*x)**2+x**
3+3*x+1)/(ln(2*x)**2+x))+(-4*x**3+10*x**2-6*x)*ln(2*x)**4+(-8*x**4+20*x**3-12*x**2-2*x)*ln(2*x)**2+(2*x-10)*ln
(2*x)-4*x**5+10*x**4-6*x**3-x**2-5*x)/((x**3+3*x)*ln(2*x)**4+(2*x**4+6*x**2+x)*ln(2*x)**2+x**5+3*x**3+x**2),x)

[Out]

Exception raised: PolynomialError

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