Optimal. Leaf size=24 \[ -\frac {48 x}{5}+\frac {3 (3-x)}{x \left (-1+\log \left (x^2\right )\right )} \]
________________________________________________________________________________________
Rubi [A] time = 0.45, antiderivative size = 33, normalized size of antiderivative = 1.38, number of steps used = 13, number of rules used = 9, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.145, Rules used = {6688, 12, 6742, 2353, 2306, 2310, 2178, 2302, 30} \begin {gather*} \frac {3}{1-\log \left (x^2\right )}-\frac {9}{x \left (1-\log \left (x^2\right )\right )}-\frac {48 x}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rule 2178
Rule 2302
Rule 2306
Rule 2310
Rule 2353
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-45+30 x-48 x^2+\left (-45+96 x^2\right ) \log \left (x^2\right )-48 x^2 \log ^2\left (x^2\right )}{5 x^2 \left (1-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {1}{5} \int \frac {-45+30 x-48 x^2+\left (-45+96 x^2\right ) \log \left (x^2\right )-48 x^2 \log ^2\left (x^2\right )}{x^2 \left (1-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {1}{5} \int \left (-48+\frac {30 (-3+x)}{x^2 \left (-1+\log \left (x^2\right )\right )^2}-\frac {45}{x^2 \left (-1+\log \left (x^2\right )\right )}\right ) \, dx\\ &=-\frac {48 x}{5}+6 \int \frac {-3+x}{x^2 \left (-1+\log \left (x^2\right )\right )^2} \, dx-9 \int \frac {1}{x^2 \left (-1+\log \left (x^2\right )\right )} \, dx\\ &=-\frac {48 x}{5}+6 \int \left (-\frac {3}{x^2 \left (-1+\log \left (x^2\right )\right )^2}+\frac {1}{x \left (-1+\log \left (x^2\right )\right )^2}\right ) \, dx-\frac {\left (9 \sqrt {x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{-x/2}}{-1+x} \, dx,x,\log \left (x^2\right )\right )}{2 x}\\ &=-\frac {48 x}{5}-\frac {9 \sqrt {x^2} \text {Ei}\left (\frac {1}{2} \left (1-\log \left (x^2\right )\right )\right )}{2 \sqrt {e} x}+6 \int \frac {1}{x \left (-1+\log \left (x^2\right )\right )^2} \, dx-18 \int \frac {1}{x^2 \left (-1+\log \left (x^2\right )\right )^2} \, dx\\ &=-\frac {48 x}{5}-\frac {9 \sqrt {x^2} \text {Ei}\left (\frac {1}{2} \left (1-\log \left (x^2\right )\right )\right )}{2 \sqrt {e} x}-\frac {9}{x \left (1-\log \left (x^2\right )\right )}+3 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-1+\log \left (x^2\right )\right )+9 \int \frac {1}{x^2 \left (-1+\log \left (x^2\right )\right )} \, dx\\ &=-\frac {48 x}{5}-\frac {9 \sqrt {x^2} \text {Ei}\left (\frac {1}{2} \left (1-\log \left (x^2\right )\right )\right )}{2 \sqrt {e} x}+\frac {3}{1-\log \left (x^2\right )}-\frac {9}{x \left (1-\log \left (x^2\right )\right )}+\frac {\left (9 \sqrt {x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{-x/2}}{-1+x} \, dx,x,\log \left (x^2\right )\right )}{2 x}\\ &=-\frac {48 x}{5}+\frac {3}{1-\log \left (x^2\right )}-\frac {9}{x \left (1-\log \left (x^2\right )\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.10, size = 24, normalized size = 1.00 \begin {gather*} \frac {1}{5} \left (-48 x-\frac {15 (-3+x)}{x \left (-1+\log \left (x^2\right )\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 33, normalized size = 1.38 \begin {gather*} -\frac {3 \, {\left (16 \, x^{2} \log \left (x^{2}\right ) - 16 \, x^{2} + 5 \, x - 15\right )}}{5 \, {\left (x \log \left (x^{2}\right ) - x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 21, normalized size = 0.88 \begin {gather*} -\frac {48}{5} \, x - \frac {3 \, {\left (x - 3\right )}}{x \log \left (x^{2}\right ) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 21, normalized size = 0.88
method | result | size |
risch | \(-\frac {48 x}{5}-\frac {3 \left (x -3\right )}{x \left (\ln \left (x^{2}\right )-1\right )}\) | \(21\) |
norman | \(\frac {9-3 x +\frac {48 x^{2}}{5}-\frac {48 x^{2} \ln \left (x^{2}\right )}{5}}{x \left (\ln \left (x^{2}\right )-1\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 30, normalized size = 1.25 \begin {gather*} -\frac {3 \, {\left (32 \, x^{2} \log \relax (x) - 16 \, x^{2} + 5 \, x - 15\right )}}{5 \, {\left (2 \, x \log \relax (x) - x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.07, size = 33, normalized size = 1.38 \begin {gather*} -\frac {\frac {48\,x^2}{5}+3\,x}{x}-\frac {3\,x-9}{x\,\left (\ln \left (x^2\right )-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 17, normalized size = 0.71 \begin {gather*} - \frac {48 x}{5} + \frac {9 - 3 x}{x \log {\left (x^{2} \right )} - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________