Optimal. Leaf size=27 \[ 5-x^2 \left (4+\frac {4}{4-x+\log (7) \log \left (\frac {4}{x}\right )}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.42, 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 {-160 x+68 x^2-8 x^3-4 x \log (7)+\left (-72 x+16 x^2\right ) \log (7) \log \left (\frac {4}{x}\right )-8 x \log ^2(7) \log ^2\left (\frac {4}{x}\right )}{16-8 x+x^2+(8-2 x) \log (7) \log \left (\frac {4}{x}\right )+\log ^2(7) \log ^2\left (\frac {4}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {68 x^2-8 x^3+x (-160-4 \log (7))+\left (-72 x+16 x^2\right ) \log (7) \log \left (\frac {4}{x}\right )-8 x \log ^2(7) \log ^2\left (\frac {4}{x}\right )}{16-8 x+x^2+(8-2 x) \log (7) \log \left (\frac {4}{x}\right )+\log ^2(7) \log ^2\left (\frac {4}{x}\right )} \, dx\\ &=\int \frac {4 x \left (17 x-2 x^2-40 \left (1+\frac {\log (7)}{40}\right )-2 (9-2 x) \log (7) \log \left (\frac {4}{x}\right )-2 \log ^2(7) \log ^2\left (\frac {4}{x}\right )\right )}{\left (4-x+\log (7) \log \left (\frac {4}{x}\right )\right )^2} \, dx\\ &=4 \int \frac {x \left (17 x-2 x^2-40 \left (1+\frac {\log (7)}{40}\right )-2 (9-2 x) \log (7) \log \left (\frac {4}{x}\right )-2 \log ^2(7) \log ^2\left (\frac {4}{x}\right )\right )}{\left (4-x+\log (7) \log \left (\frac {4}{x}\right )\right )^2} \, dx\\ &=4 \int \left (-2 x-\frac {x (x+\log (7))}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2}+\frac {2 x}{-4+x-\log (7) \log \left (\frac {4}{x}\right )}\right ) \, dx\\ &=-4 x^2-4 \int \frac {x (x+\log (7))}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2} \, dx+8 \int \frac {x}{-4+x-\log (7) \log \left (\frac {4}{x}\right )} \, dx\\ &=-4 x^2-4 \int \left (\frac {x^2}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2}+\frac {x \log (7)}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2}\right ) \, dx+8 \int \frac {x}{-4+x-\log (7) \log \left (\frac {4}{x}\right )} \, dx\\ &=-4 x^2-4 \int \frac {x^2}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2} \, dx+8 \int \frac {x}{-4+x-\log (7) \log \left (\frac {4}{x}\right )} \, dx-(4 \log (7)) \int \frac {x}{\left (-4+x-\log (7) \log \left (\frac {4}{x}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.08, size = 26, normalized size = 0.96 \begin {gather*} -4 \left (x^2+\frac {x^2}{4-x+\log (7) \log \left (\frac {4}{x}\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 3.56, size = 48, normalized size = 1.78
method | result | size |
risch | \(-4 x^{2}-\frac {4 x^{2}}{4+\ln \left (7\right ) \ln \left (\frac {4}{x}\right )-x}\) | \(28\) |
norman | \(\frac {-20 x^{2}+4 x^{3}-4 \ln \left (7\right ) \ln \left (\frac {4}{x}\right ) x^{2}}{4+\ln \left (7\right ) \ln \left (\frac {4}{x}\right )-x}\) | \(42\) |
derivativedivides | \(\frac {4 \left (4-\frac {4 \ln \left (7\right ) \ln \left (\frac {4}{x}\right )}{x}-\frac {20}{x}\right ) x^{2}}{\frac {4 \ln \left (7\right ) \ln \left (\frac {4}{x}\right )}{x}+\frac {16}{x}-4}\) | \(48\) |
default | \(\frac {4 \left (4-\frac {4 \ln \left (7\right ) \ln \left (\frac {4}{x}\right )}{x}-\frac {20}{x}\right ) x^{2}}{\frac {4 \ln \left (7\right ) \ln \left (\frac {4}{x}\right )}{x}+\frac {16}{x}-4}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.53, size = 46, normalized size = 1.70 \begin {gather*} \frac {4 \, {\left (x^{2} \log \left (7\right ) \log \left (x\right ) - {\left (2 \, \log \left (7\right ) \log \left (2\right ) + 5\right )} x^{2} + x^{3}\right )}}{2 \, \log \left (7\right ) \log \left (2\right ) - \log \left (7\right ) \log \left (x\right ) - x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 41, normalized size = 1.52 \begin {gather*} -\frac {4 \, {\left (x^{2} \log \left (7\right ) \log \left (\frac {4}{x}\right ) - x^{3} + 5 \, x^{2}\right )}}{\log \left (7\right ) \log \left (\frac {4}{x}\right ) - x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.07, size = 22, normalized size = 0.81 \begin {gather*} - 4 x^{2} - \frac {4 x^{2}}{- x + \log {\left (7 \right )} \log {\left (\frac {4}{x} \right )} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 33, normalized size = 1.22 \begin {gather*} -4 \, x^{2} - \frac {4}{\frac {\log \left (7\right ) \log \left (\frac {4}{x}\right )}{x^{2}} - \frac {1}{x} + \frac {4}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.54, size = 85, normalized size = 3.15 \begin {gather*} 8\,x-\frac {\frac {8\,x^2\,\ln \left (\frac {4}{x}\right )}{x+\ln \left (7\right )}+\frac {4\,x\,\left (8\,x+x\,\ln \left (7\right )-x^2\right )}{\ln \left (7\right )\,\left (x+\ln \left (7\right )\right )}}{\ln \left (\frac {4}{x}\right )-\frac {x-4}{\ln \left (7\right )}}+\frac {8\,{\ln \left (7\right )}^2}{x+\ln \left (7\right )}-4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________