Optimal. Leaf size=23 \[ x^2-\frac {4-\frac {3}{-3+\frac {x}{\log ^2(2)}}}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.09, antiderivative size = 38, normalized size of antiderivative = 1.65, number of steps
used = 4, number of rules used = 3, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1608, 27, 1634}
\begin {gather*} x^2-\frac {5}{x^2}+\frac {1}{3 \log ^2(2) \left (x-3 \log ^2(2)\right )}-\frac {1}{3 x \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 1608
Rule 1634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 x^2+2 x^6+\left (-57 x-12 x^5\right ) \log ^2(2)+\left (90+18 x^4\right ) \log ^4(2)}{x^3 \left (x^2-6 x \log ^2(2)+9 \log ^4(2)\right )} \, dx\\ &=\int \frac {8 x^2+2 x^6+\left (-57 x-12 x^5\right ) \log ^2(2)+\left (90+18 x^4\right ) \log ^4(2)}{x^3 \left (x-3 \log ^2(2)\right )^2} \, dx\\ &=\int \left (\frac {10}{x^3}+2 x+\frac {1}{3 x^2 \log ^2(2)}-\frac {1}{3 \log ^2(2) \left (-x+3 \log ^2(2)\right )^2}\right ) \, dx\\ &=-\frac {5}{x^2}+x^2-\frac {1}{3 x \log ^2(2)}+\frac {1}{3 \log ^2(2) \left (x-3 \log ^2(2)\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 38, normalized size = 1.65 \begin {gather*} -\frac {5}{x^2}+x^2-\frac {1}{3 x \log ^2(2)}+\frac {1}{3 \log ^2(2) \left (x-3 \log ^2(2)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.36, size = 35, normalized size = 1.52
method | result | size |
risch | \(x^{2}+\frac {-15 \ln \left (2\right )^{2}+4 x}{x^{2} \left (3 \ln \left (2\right )^{2}-x \right )}\) | \(32\) |
default | \(x^{2}+\frac {1}{3 \ln \left (2\right )^{2} \left (-3 \ln \left (2\right )^{2}+x \right )}-\frac {5}{x^{2}}-\frac {1}{3 \ln \left (2\right )^{2} x}\) | \(35\) |
gosper | \(\frac {-x^{5}+3 x^{4} \ln \left (2\right )^{2}+4 x -15 \ln \left (2\right )^{2}}{x^{2} \left (3 \ln \left (2\right )^{2}-x \right )}\) | \(41\) |
norman | \(\frac {-x^{5}+3 x^{4} \ln \left (2\right )^{2}+4 x -15 \ln \left (2\right )^{2}}{x^{2} \left (3 \ln \left (2\right )^{2}-x \right )}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 33, normalized size = 1.43 \begin {gather*} x^{2} - \frac {15 \, \log \left (2\right )^{2} - 4 \, x}{3 \, x^{2} \log \left (2\right )^{2} - x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 37, normalized size = 1.61 \begin {gather*} -\frac {x^{5} - 3 \, {\left (x^{4} - 5\right )} \log \left (2\right )^{2} - 4 \, x}{3 \, x^{2} \log \left (2\right )^{2} - x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.18, size = 26, normalized size = 1.13 \begin {gather*} x^{2} + \frac {- 4 x + 15 \log {\left (2 \right )}^{2}}{x^{3} - 3 x^{2} \log {\left (2 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 39, normalized size = 1.70 \begin {gather*} x^{2} - \frac {1}{3 \, {\left (3 \, \log \left (2\right )^{2} - x\right )} \log \left (2\right )^{2}} - \frac {15 \, \log \left (2\right )^{2} + x}{3 \, x^{2} \log \left (2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.39, size = 29, normalized size = 1.26 \begin {gather*} x^2-\frac {4\,x-15\,{\ln \left (2\right )}^2}{x^2\,\left (x-3\,{\ln \left (2\right )}^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________