Optimal. Leaf size=18 \[ 4+\log \left (2+e^{4+\frac {16}{5} \log (4) \log (x)}+x\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.31, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {6741, 12, 6684} \begin {gather*} \log \left (x+e^4 2^{\frac {32 \log (x)}{5}}+2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 x+16 e^{\frac {2}{5} (10+8 \log (4) \log (x))} \log (4)}{5 x \left (2+e^{4+\frac {16}{5} \log (4) \log (x)}+x\right )} \, dx\\ &=\frac {1}{5} \int \frac {5 x+16 e^{\frac {2}{5} (10+8 \log (4) \log (x))} \log (4)}{x \left (2+e^{4+\frac {16}{5} \log (4) \log (x)}+x\right )} \, dx\\ &=\log \left (2+2^{\frac {32 \log (x)}{5}} e^4+x\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.30, size = 16, normalized size = 0.89 \begin {gather*} \log \left (2+e^{4+\frac {16}{5} \log (4) \log (x)}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 13, normalized size = 0.72 \begin {gather*} \log \left (x + e^{\left (\frac {32}{5} \, \log \relax (2) \log \relax (x) + 4\right )} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 13, normalized size = 0.72 \begin {gather*} \log \left (x + e^{\left (\frac {32}{5} \, \log \relax (2) \log \relax (x) + 4\right )} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.11, size = 16, normalized size = 0.89
method | result | size |
norman | \(\ln \left (2+{\mathrm e}^{\frac {32 \ln \relax (2) \ln \relax (x )}{5}+4}+x \right )\) | \(16\) |
risch | \(-4+\ln \left (x^{\frac {32 \ln \relax (2)}{5}} {\mathrm e}^{4}+x +2\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 16, normalized size = 0.89 \begin {gather*} \log \left ({\left (x + e^{\left (\frac {32}{5} \, \log \relax (2) \log \relax (x) + 4\right )} + 2\right )} e^{\left (-4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.73, size = 13, normalized size = 0.72 \begin {gather*} \ln \left (x+{\mathrm {e}}^{\frac {32\,\ln \relax (2)\,\ln \relax (x)}{5}+4}+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 3.22, size = 19, normalized size = 1.06 \begin {gather*} \log {\left (x + e^{4} e^{\frac {32 \log {\relax (2 )} \log {\relax (x )}}{5}} + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________