Optimal. Leaf size=24 \[ \left (e^{12}+x\right )^2+5 \left (4-\log \left (x \left (8-2 x^2\right )\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {1607, 1816,
266} \begin {gather*} x^2-5 \log \left (4-x^2\right )+2 e^{12} x-5 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 1607
Rule 1816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20-23 x^2+2 x^4+e^{12} \left (-8 x+2 x^3\right )}{x \left (-4+x^2\right )} \, dx\\ &=\int \left (2 e^{12}-\frac {5}{x}+2 x-\frac {10 x}{-4+x^2}\right ) \, dx\\ &=2 e^{12} x+x^2-5 \log (x)-10 \int \frac {x}{-4+x^2} \, dx\\ &=2 e^{12} x+x^2-5 \log (x)-5 \log \left (4-x^2\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} 2 e^{12} x+x^2-5 \log (x)-5 \log \left (4-x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.66, size = 26, normalized size = 1.08
method | result | size |
risch | \(2 x \,{\mathrm e}^{12}+x^{2}-5 \ln \left (x^{3}-4 x \right )\) | \(20\) |
default | \(x^{2}+2 x \,{\mathrm e}^{12}-5 \ln \left (x -2\right )-5 \ln \left (2+x \right )-5 \ln \left (x \right )\) | \(26\) |
norman | \(x^{2}+2 x \,{\mathrm e}^{12}-5 \ln \left (x -2\right )-5 \ln \left (2+x \right )-5 \ln \left (x \right )\) | \(26\) |
meijerg | \(-5 \ln \left (1-\frac {x^{2}}{4}\right )-5 \ln \left (x \right )+5 \ln \left (2\right )-\frac {5 i \pi }{2}-2 i {\mathrm e}^{12} \left (i x -2 i \arctanh \left (\frac {x}{2}\right )\right )+4 \,{\mathrm e}^{12} \arctanh \left (\frac {x}{2}\right )+x^{2}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 25, normalized size = 1.04 \begin {gather*} x^{2} + 2 \, x e^{12} - 5 \, \log \left (x + 2\right ) - 5 \, \log \left (x - 2\right ) - 5 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.34, size = 19, normalized size = 0.79 \begin {gather*} x^{2} + 2 \, x e^{12} - 5 \, \log \left (x^{3} - 4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 19, normalized size = 0.79 \begin {gather*} x^{2} + 2 x e^{12} - 5 \log {\left (x^{3} - 4 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 28, normalized size = 1.17 \begin {gather*} x^{2} + 2 \, x e^{12} - 5 \, \log \left ({\left | x + 2 \right |}\right ) - 5 \, \log \left ({\left | x - 2 \right |}\right ) - 5 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.08, size = 19, normalized size = 0.79 \begin {gather*} 2\,x\,{\mathrm {e}}^{12}-5\,\ln \left (x^3-4\,x\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________