Optimal. Leaf size=22 \[ -3+2 x+\log \left (\log \left (4-x-e x^2-\log (x)\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.34, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 3, number of rules used = 2, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6874, 6816}
\begin {gather*} \log \left (\log \left (-e x^2-x-\log (x)+4\right )\right )+2 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2+\frac {1+x+2 e x^2}{x \left (-4+x+e x^2+\log (x)\right ) \log \left (4-x-e x^2-\log (x)\right )}\right ) \, dx\\ &=2 x+\int \frac {1+x+2 e x^2}{x \left (-4+x+e x^2+\log (x)\right ) \log \left (4-x-e x^2-\log (x)\right )} \, dx\\ &=2 x+\log \left (\log \left (4-x-e x^2-\log (x)\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.07, size = 21, normalized size = 0.95 \begin {gather*} 2 x+\log \left (\log \left (4-x-e x^2-\log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.01, size = 23, normalized size = 1.05
method | result | size |
default | \(2 x +\ln \left (\ln \left (-\ln \left (x \right )-x^{2} {\mathrm e}-x +4\right )\right )\) | \(23\) |
risch | \(2 x +\ln \left (\ln \left (-\ln \left (x \right )-x^{2} {\mathrm e}-x +4\right )\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.34, size = 22, normalized size = 1.00 \begin {gather*} 2 \, x + \log \left (\log \left (-x^{2} e - x - \log \left (x\right ) + 4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 22, normalized size = 1.00 \begin {gather*} 2 \, x + \log \left (\log \left (-x^{2} e - x - \log \left (x\right ) + 4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.19, size = 19, normalized size = 0.86 \begin {gather*} 2 x + \log {\left (\log {\left (- e x^{2} - x - \log {\left (x \right )} + 4 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 22, normalized size = 1.00 \begin {gather*} 2 \, x + \log \left (\log \left (-x^{2} e - x - \log \left (x\right ) + 4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.03, size = 22, normalized size = 1.00 \begin {gather*} 2\,x+\ln \left (\ln \left (4-\ln \left (x\right )-x^2\,\mathrm {e}-x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________