Optimal. Leaf size=23 \[ \frac {-4+x}{-4-x+x^2-e^6 \log (3)+\log (x)} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.07, 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 {4-9 x+8 x^2-x^3-e^6 x \log (3)+x \log (x)}{16 x+8 x^2-7 x^3-2 x^4+x^5+e^6 \left (8 x+2 x^2-2 x^3\right ) \log (3)+e^{12} x \log ^2(3)+\left (-8 x-2 x^2+2 x^3-2 e^6 x \log (3)\right ) \log (x)+x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4+8 x^2-x^3+x \left (-9-e^6 \log (3)\right )+x \log (x)}{16 x+8 x^2-7 x^3-2 x^4+x^5+e^6 \left (8 x+2 x^2-2 x^3\right ) \log (3)+e^{12} x \log ^2(3)+\left (-8 x-2 x^2+2 x^3-2 e^6 x \log (3)\right ) \log (x)+x \log ^2(x)} \, dx\\ &=\int \frac {4+8 x^2-x^3+x \left (-9-e^6 \log (3)\right )+x \log (x)}{8 x^2-7 x^3-2 x^4+x^5+e^6 \left (8 x+2 x^2-2 x^3\right ) \log (3)+x \left (16+e^{12} \log ^2(3)\right )+\left (-8 x-2 x^2+2 x^3-2 e^6 x \log (3)\right ) \log (x)+x \log ^2(x)} \, dx\\ &=\int \frac {4+8 x^2-x^3-x \left (9+e^6 \log (3)\right )+x \log (x)}{x \left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx\\ &=\int \left (\frac {4-5 x+9 x^2-2 x^3}{x \left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2}+\frac {1}{-x+x^2-4 \left (1+\frac {1}{4} e^6 \log (3)\right )+\log (x)}\right ) \, dx\\ &=\int \frac {4-5 x+9 x^2-2 x^3}{x \left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx+\int \frac {1}{-x+x^2-4 \left (1+\frac {1}{4} e^6 \log (3)\right )+\log (x)} \, dx\\ &=\int \left (-\frac {5}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2}+\frac {4}{x \left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2}+\frac {9 x}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2}-\frac {2 x^2}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2}\right ) \, dx+\int \frac {1}{-x+x^2-4 \left (1+\frac {1}{4} e^6 \log (3)\right )+\log (x)} \, dx\\ &=-\left (2 \int \frac {x^2}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx\right )+4 \int \frac {1}{x \left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx-5 \int \frac {1}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx+9 \int \frac {x}{\left (x-x^2+4 \left (1+\frac {1}{4} e^6 \log (3)\right )-\log (x)\right )^2} \, dx+\int \frac {1}{-x+x^2-4 \left (1+\frac {1}{4} e^6 \log (3)\right )+\log (x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.15, size = 23, normalized size = 1.00 \begin {gather*} \frac {-4+x}{-4-x+x^2-e^6 \log (3)+\log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 3.19, size = 28, normalized size = 1.22
method | result | size |
risch | \(-\frac {x -4}{{\mathrm e}^{6} \ln \left (3\right )-x^{2}+x -\ln \left (x \right )+4}\) | \(25\) |
default | \(\frac {-x +4}{{\mathrm e}^{6} \ln \left (3\right )-x^{2}+x -\ln \left (x \right )+4}\) | \(28\) |
norman | \(\frac {-x +4}{{\mathrm e}^{6} \ln \left (3\right )-x^{2}+x -\ln \left (x \right )+4}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.50, size = 22, normalized size = 0.96 \begin {gather*} \frac {x - 4}{x^{2} - e^{6} \log \left (3\right ) - x + \log \left (x\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 22, normalized size = 0.96 \begin {gather*} \frac {x - 4}{x^{2} - e^{6} \log \left (3\right ) - x + \log \left (x\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 19, normalized size = 0.83 \begin {gather*} \frac {x - 4}{x^{2} - x + \log {\left (x \right )} - e^{6} \log {\left (3 \right )} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 22, normalized size = 0.96 \begin {gather*} \frac {x - 4}{x^{2} - e^{6} \log \left (3\right ) - x + \log \left (x\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.60, size = 24, normalized size = 1.04 \begin {gather*} -\frac {x-4}{x-\ln \left (x\right )+{\mathrm {e}}^6\,\ln \left (3\right )-x^2+4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________