Optimal. Leaf size=25 \[ x (-2+4 x)+\frac {x^2 \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^2(x)} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.60, 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 (2 x^2+8 x^5\right ) \log (x)+\left (6-26 x+8 x^2-2 x^4+8 x^5\right ) \log ^3(x)+\left (6 x-2 x^2-2 x^5+\left (-6 x+2 x^2+2 x^5\right ) \log (x)\right ) \log \left (9-6 x+x^2-6 x^4+2 x^5+x^8\right )}{\left (-3+x+x^4\right ) \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 \left (x^2+4 x^5\right ) \log (x)-\left (6-26 x+8 x^2-2 x^4+8 x^5\right ) \log ^3(x)-2 x \left (-3+x+x^4\right ) (-1+\log (x)) \log \left (\left (-3+x+x^4\right )^2\right )}{\left (3-x-x^4\right ) \log ^3(x)} \, dx\\ &=\int 2 \left (-1+4 x+\frac {x^2+4 x^5}{\left (-3+x+x^4\right ) \log ^2(x)}+\frac {x (-1+\log (x)) \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^3(x)}\right ) \, dx\\ &=2 \int \left (-1+4 x+\frac {x^2+4 x^5}{\left (-3+x+x^4\right ) \log ^2(x)}+\frac {x (-1+\log (x)) \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^3(x)}\right ) \, dx\\ &=-2 x+4 x^2+2 \int \frac {x^2+4 x^5}{\left (-3+x+x^4\right ) \log ^2(x)} \, dx+2 \int \frac {x (-1+\log (x)) \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^3(x)} \, dx\\ &=-2 x+4 x^2+2 \int \frac {x^2 \left (1+4 x^3\right )}{\left (-3+x+x^4\right ) \log ^2(x)} \, dx+2 \int \left (-\frac {x \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^3(x)}+\frac {x \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^2(x)}\right ) \, dx\\ &=-2 x+4 x^2+2 \int \frac {x^2 \left (1+4 x^3\right )}{\left (-3+x+x^4\right ) \log ^2(x)} \, dx-2 \int \frac {x \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^3(x)} \, dx+2 \int \frac {x \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^2(x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.11, size = 26, normalized size = 1.04 \begin {gather*} -2 x+4 x^2+\frac {x^2 \log \left (\left (-3+x+x^4\right )^2\right )}{\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.88, size = 116, normalized size = 4.64
method | result | size |
risch | \(\frac {2 x^{2} \ln \left (x^{4}+x -3\right )}{\ln \left (x \right )^{2}}+\frac {x \left (-i \pi x \mathrm {csgn}\left (i \left (x^{4}+x -3\right )\right )^{2} \mathrm {csgn}\left (i \left (x^{4}+x -3\right )^{2}\right )+2 i \pi x \,\mathrm {csgn}\left (i \left (x^{4}+x -3\right )\right ) \mathrm {csgn}\left (i \left (x^{4}+x -3\right )^{2}\right )^{2}-i \pi x \mathrm {csgn}\left (i \left (x^{4}+x -3\right )^{2}\right )^{3}+8 x \ln \left (x \right )^{2}-4 \ln \left (x \right )^{2}\right )}{2 \ln \left (x \right )^{2}}\) | \(116\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.33, size = 32, normalized size = 1.28 \begin {gather*} \frac {2 \, {\left (x^{2} \log \left (x^{4} + x - 3\right ) + {\left (2 \, x^{2} - x\right )} \log \left (x\right )^{2}\right )}}{\log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.31, size = 47, normalized size = 1.88 \begin {gather*} \frac {x^{2} \log \left (x^{8} + 2 \, x^{5} - 6 \, x^{4} + x^{2} - 6 \, x + 9\right ) + 2 \, {\left (2 \, x^{2} - x\right )} \log \left (x\right )^{2}}{\log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.26, size = 39, normalized size = 1.56 \begin {gather*} 4 x^{2} + \frac {x^{2} \log {\left (x^{8} + 2 x^{5} - 6 x^{4} + x^{2} - 6 x + 9 \right )}}{\log {\left (x \right )}^{2}} - 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 39, normalized size = 1.56 \begin {gather*} 4 \, x^{2} - 2 \, x + \frac {x^{2} \log \left (x^{8} + 2 \, x^{5} - 6 \, x^{4} + x^{2} - 6 \, x + 9\right )}{\log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.48, size = 39, normalized size = 1.56 \begin {gather*} 4\,x^2-2\,x+\frac {x^2\,\ln \left (x^8+2\,x^5-6\,x^4+x^2-6\,x+9\right )}{{\ln \left (x\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________