3.57.47 \(\int \frac {(-30-12 x^2-6 x^3+6 x^4) \log ^2(\frac {5+2 x^2+x^3-x^4}{x^2})+\log (\frac {2}{x}) ((60-6 x^3+12 x^4) \log (\frac {5+2 x^2+x^3-x^4}{x^2})+(30+12 x^2+6 x^3-6 x^4) \log ^2(\frac {5+2 x^2+x^3-x^4}{x^2}))}{(-5 x^3-2 x^5-x^6+x^7) \log ^3(\frac {2}{x})} \, dx\)

Optimal. Leaf size=29 \[ \frac {3 \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^2 \log ^2\left (\frac {2}{x}\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 3.38, 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 {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-30 - 12*x^2 - 6*x^3 + 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2 + Log[2/x]*((60 - 6*x^3 + 12*x^4)*Log[(
5 + 2*x^2 + x^3 - x^4)/x^2] + (30 + 12*x^2 + 6*x^3 - 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2))/((-5*x^3 - 2*
x^5 - x^6 + x^7)*Log[2/x]^3),x]

[Out]

-12*Defer[Int][Log[2 + 5/x^2 + x - x^2]/(x^3*Log[2/x]^2), x] + (24*Defer[Int][Log[2 + 5/x^2 + x - x^2]/(x*Log[
2/x]^2), x])/5 - 18*Defer[Int][Log[2 + 5/x^2 + x - x^2]/((-5 - 2*x^2 - x^3 + x^4)*Log[2/x]^2), x] + (168*Defer
[Int][(x*Log[2 + 5/x^2 + x - x^2])/((-5 - 2*x^2 - x^3 + x^4)*Log[2/x]^2), x])/5 + (24*Defer[Int][(x^2*Log[2 +
5/x^2 + x - x^2])/((-5 - 2*x^2 - x^3 + x^4)*Log[2/x]^2), x])/5 - (24*Defer[Int][(x^3*Log[2 + 5/x^2 + x - x^2])
/((-5 - 2*x^2 - x^3 + x^4)*Log[2/x]^2), x])/5 + 6*Defer[Int][Log[2 + 5/x^2 + x - x^2]^2/(x^3*Log[2/x]^3), x] -
6*Defer[Int][Log[2 + 5/x^2 + x - x^2]^2/(x^3*Log[2/x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\left (\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )-\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{x^3 \left (5+2 x^2+x^3-x^4\right ) \log ^3\left (\frac {2}{x}\right )} \, dx\\ &=\int \left (\frac {6 \left (10-x^3+2 x^4\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {6 \left (-1+\log \left (\frac {2}{x}\right )\right ) \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )}\right ) \, dx\\ &=6 \int \frac {\left (10-x^3+2 x^4\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\left (-1+\log \left (\frac {2}{x}\right )\right ) \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx\\ &=6 \int \left (-\frac {2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )}+\frac {4 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{5 x \log ^2\left (\frac {2}{x}\right )}-\frac {\left (15-28 x-4 x^2+4 x^3\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{5 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}\right ) \, dx-6 \int \left (-\frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )}+\frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )}\right ) \, dx\\ &=-\left (\frac {6}{5} \int \frac {\left (15-28 x-4 x^2+4 x^3\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx\right )+\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx\\ &=-\left (\frac {6}{5} \int \left (\frac {15 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {28 x \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {4 x^2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}+\frac {4 x^3 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}\right ) \, dx\right )+\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx\\ &=\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+\frac {24}{5} \int \frac {x^2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx-\frac {24}{5} \int \frac {x^3 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-18 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx+\frac {168}{5} \int \frac {x \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [F]  time = 0.15, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[((-30 - 12*x^2 - 6*x^3 + 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2 + Log[2/x]*((60 - 6*x^3 + 12*x^4)
*Log[(5 + 2*x^2 + x^3 - x^4)/x^2] + (30 + 12*x^2 + 6*x^3 - 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2))/((-5*x^
3 - 2*x^5 - x^6 + x^7)*Log[2/x]^3),x]

[Out]

Integrate[((-30 - 12*x^2 - 6*x^3 + 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2 + Log[2/x]*((60 - 6*x^3 + 12*x^4)
*Log[(5 + 2*x^2 + x^3 - x^4)/x^2] + (30 + 12*x^2 + 6*x^3 - 6*x^4)*Log[(5 + 2*x^2 + x^3 - x^4)/x^2]^2))/((-5*x^
3 - 2*x^5 - x^6 + x^7)*Log[2/x]^3), x]

________________________________________________________________________________________

fricas [A]  time = 0.57, size = 36, normalized size = 1.24 \begin {gather*} \frac {3 \, \log \left (-\frac {x^{4} - x^{3} - 2 \, x^{2} - 5}{x^{2}}\right )^{2}}{x^{2} \log \left (\frac {2}{x}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^4+6*x^3+12*x^2+30)*log((-x^4+x^3+2*x^2+5)/x^2)^2+(12*x^4-6*x^3+60)*log((-x^4+x^3+2*x^2+5)/x^
2))*log(2/x)+(6*x^4-6*x^3-12*x^2-30)*log((-x^4+x^3+2*x^2+5)/x^2)^2)/(x^7-x^6-2*x^5-5*x^3)/log(2/x)^3,x, algori
thm="fricas")

[Out]

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

________________________________________________________________________________________

giac [B]  time = 1.30, size = 143, normalized size = 4.93 \begin {gather*} \frac {3 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right )^{2}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} - \frac {12 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right ) \log \relax (x)}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} - \frac {12 \, {\left (\log \relax (2)^{2} - 2 \, \log \relax (2) \log \relax (x)\right )}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} + \frac {12}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^4+6*x^3+12*x^2+30)*log((-x^4+x^3+2*x^2+5)/x^2)^2+(12*x^4-6*x^3+60)*log((-x^4+x^3+2*x^2+5)/x^
2))*log(2/x)+(6*x^4-6*x^3-12*x^2-30)*log((-x^4+x^3+2*x^2+5)/x^2)^2)/(x^7-x^6-2*x^5-5*x^3)/log(2/x)^3,x, algori
thm="giac")

[Out]

3*log(-x^4 + x^3 + 2*x^2 + 5)^2/(x^2*log(2)^2 - 2*x^2*log(2)*log(x) + x^2*log(x)^2) - 12*log(-x^4 + x^3 + 2*x^
2 + 5)*log(x)/(x^2*log(2)^2 - 2*x^2*log(2)*log(x) + x^2*log(x)^2) - 12*(log(2)^2 - 2*log(2)*log(x))/(x^2*log(2
)^2 - 2*x^2*log(2)*log(x) + x^2*log(x)^2) + 12/x^2

________________________________________________________________________________________

maple [C]  time = 2.35, size = 2291, normalized size = 79.00

method	result	size
risch	\(\text {Expression too large to display}\)	\(2291\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-6*x^4+6*x^3+12*x^2+30)*ln((-x^4+x^3+2*x^2+5)/x^2)^2+(12*x^4-6*x^3+60)*ln((-x^4+x^3+2*x^2+5)/x^2))*ln(2
/x)+(6*x^4-6*x^3-12*x^2-30)*ln((-x^4+x^3+2*x^2+5)/x^2)^2)/(x^7-x^6-2*x^5-5*x^3)/ln(2/x)^3,x,method=_RETURNVERB
OSE)

[Out]

-12/x^2/(2*I*ln(2)-2*I*ln(x))^2*ln(x^4-x^3-2*x^2-5)^2-12*(2*I*Pi*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-I*Pi*csgn(I/x
^2*(x^4-x^3-2*x^2-5))^3-I*Pi*csgn(I/x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-I*Pi*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I
/x^2*(x^4-x^3-2*x^2-5))^2-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-2*I*Pi+4*ln(x)-I*Pi*csgn
(I*x^2)^3+I*Pi*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5)))/x^2/(-2*ln(2)+2*ln(x))^2*l
n(x^4-x^3-2*x^2-5)+3*(-Pi^2*csgn(I*x)^4*csgn(I*x^2)^2+4*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^2*csgn(I*x)^2*csgn
(I*x^2)^4+4*Pi^2*csgn(I*x)*csgn(I*x^2)^5-4*Pi^2+16*ln(x)^2-8*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/x^2*(x^4-x^3-
2*x^2-5))^2-Pi^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^6-4*Pi^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^4+4*Pi^2*csgn(I/x^2*(x^4
-x^3-2*x^2-5))^5-4*Pi^2*csgn(I*x)^2*csgn(I*x^2)+8*Pi^2*csgn(I*x)*csgn(I*x^2)^2-4*Pi^2*csgn(I/x^2)*csgn(I/x^2*(
x^4-x^3-2*x^2-5))^2-4*Pi^2*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-2*Pi^2*csgn(I*x^2)^3*csgn
(I/x^2*(x^4-x^3-2*x^2-5))^3-Pi^2*csgn(I/x^2)^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^4-2*Pi^2*csgn(I/x^2)*csgn(I/x^2*(
x^4-x^3-2*x^2-5))^5-Pi^2*csgn(I*(x^4-x^3-2*x^2-5))^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^4-2*Pi^2*csgn(I*(x^4-x^3-2*
x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^5+4*Pi^2*csgn(I/x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^4+4*Pi^2*csgn(I*(x^4-
x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^4-Pi^2*csgn(I*x^2)^6-2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/x^2)*cs
gn(I/x^2*(x^4-x^3-2*x^2-5))^2-2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x
^2-5))^2+4*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2+4*Pi^2*csgn(I*x)*csgn(I*x^
2)^2*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2+2*Pi^2*csgn(I*x^2)^3*csgn(I/x^2)*csgn(I*(x^4-x^
3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))-4*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))
*csgn(I/x^2*(x^4-x^3-2*x^2-5))+4*Pi^2*csgn(I*x)*csgn(I*x^2)^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^3+4*Pi^2*csgn(I*x^
2)^3*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2+8*I*ln(x)*Pi*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*
x^2-5))-16*I*Pi*ln(x)+8*Pi^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-4*Pi^2*csgn(I*x^2)^3-8*I*ln(x)*Pi*csgn(I/x^2*(x^4
-x^3-2*x^2-5))^3-8*I*ln(x)*Pi*csgn(I*x)^2*csgn(I*x^2)+16*I*ln(x)*Pi*csgn(I*x)*csgn(I*x^2)^2-8*I*ln(x)*Pi*csgn(
I/x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-8*I*ln(x)*Pi*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-
4*Pi^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^3+4*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-4*Pi^2*c
sgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^3-2*Pi^2*csgn(I*x^2)^3*csgn(I/x^2)*csgn(I/x
^2*(x^4-x^3-2*x^2-5))^2-2*Pi^2*csgn(I*x^2)^3*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-Pi^2*cs
gn(I/x^2)^2*csgn(I*(x^4-x^3-2*x^2-5))^2*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2+2*Pi^2*csgn(I/x^2)^2*csgn(I*(x^4-x^3-2
*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))^3+2*Pi^2*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))^2*csgn(I/x^2*(x^4-x^3-2*
x^2-5))^3+4*Pi^2*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5))-8*I*ln(x)*Pi*csgn(I*x^2)^
3+16*I*ln(x)*Pi*csgn(I/x^2*(x^4-x^3-2*x^2-5))^2-2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/x^2*(x^4-x^3-2*x^2-5))^3
+2*Pi^2*csgn(I*x)^2*csgn(I*x^2)*csgn(I/x^2)*csgn(I*(x^4-x^3-2*x^2-5))*csgn(I/x^2*(x^4-x^3-2*x^2-5)))/x^2/(-2*l
n(2)+2*ln(x))^2

________________________________________________________________________________________

maxima [B]  time = 0.54, size = 75, normalized size = 2.59 \begin {gather*} \frac {3 \, {\left (\log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right )^{2} - 4 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right ) \log \relax (x) + 4 \, \log \relax (x)^{2}\right )}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^4+6*x^3+12*x^2+30)*log((-x^4+x^3+2*x^2+5)/x^2)^2+(12*x^4-6*x^3+60)*log((-x^4+x^3+2*x^2+5)/x^
2))*log(2/x)+(6*x^4-6*x^3-12*x^2-30)*log((-x^4+x^3+2*x^2+5)/x^2)^2)/(x^7-x^6-2*x^5-5*x^3)/log(2/x)^3,x, algori
thm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 3.85, size = 35, normalized size = 1.21 \begin {gather*} \frac {3\,{\ln \left (\frac {-x^4+x^3+2\,x^2+5}{x^2}\right )}^2}{x^2\,{\ln \left (\frac {2}{x}\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((2*x^2 + x^3 - x^4 + 5)/x^2)^2*(12*x^2 + 6*x^3 - 6*x^4 + 30) - log(2/x)*(log((2*x^2 + x^3 - x^4 + 5)/
x^2)^2*(12*x^2 + 6*x^3 - 6*x^4 + 30) + log((2*x^2 + x^3 - x^4 + 5)/x^2)*(12*x^4 - 6*x^3 + 60)))/(log(2/x)^3*(5
*x^3 + 2*x^5 + x^6 - x^7)),x)

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.50, size = 31, normalized size = 1.07 \begin {gather*} \frac {3 \log {\left (\frac {- x^{4} + x^{3} + 2 x^{2} + 5}{x^{2}} \right )}^{2}}{x^{2} \log {\left (\frac {2}{x} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x**4+6*x**3+12*x**2+30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2+(12*x**4-6*x**3+60)*ln((-x**4+x**3+2
*x**2+5)/x**2))*ln(2/x)+(6*x**4-6*x**3-12*x**2-30)*ln((-x**4+x**3+2*x**2+5)/x**2)**2)/(x**7-x**6-2*x**5-5*x**3
)/ln(2/x)**3,x)

[Out]

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

________________________________________________________________________________________