Optimal. Leaf size=23 \[ 2 \left (-3-\frac {e^{5/2}}{x^2}+2 x+\log \left (25 x^3\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {14} \begin {gather*} -\frac {2 e^{5/2}}{x^2}+4 x+6 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4+\frac {4 e^{5/2}}{x^3}+\frac {6}{x}\right ) \, dx\\ &=-\frac {2 e^{5/2}}{x^2}+4 x+6 \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 18, normalized size = 0.78 \begin {gather*} -\frac {2 e^{5/2}}{x^2}+4 x+6 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.08, size = 22, normalized size = 0.96 \begin {gather*} \frac {2 \, {\left (2 \, x^{3} + 3 \, x^{2} \log \relax (x) - e^{\frac {5}{2}}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 16, normalized size = 0.70 \begin {gather*} 4 \, x - \frac {2 \, e^{\frac {5}{2}}}{x^{2}} + 6 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 16, normalized size = 0.70
method | result | size |
default | \(4 x +6 \ln \relax (x )-\frac {2 \,{\mathrm e}^{\frac {5}{2}}}{x^{2}}\) | \(16\) |
risch | \(4 x +6 \ln \relax (x )-\frac {2 \,{\mathrm e}^{\frac {5}{2}}}{x^{2}}\) | \(16\) |
norman | \(\frac {4 x^{3}-2 \,{\mathrm e}^{\frac {5}{2}}}{x^{2}}+6 \ln \relax (x )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.54, size = 15, normalized size = 0.65 \begin {gather*} 4 \, x - \frac {2 \, e^{\frac {5}{2}}}{x^{2}} + 6 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 15, normalized size = 0.65 \begin {gather*} 4\,x+6\,\ln \relax (x)-\frac {2\,{\mathrm {e}}^{5/2}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 17, normalized size = 0.74 \begin {gather*} 4 x + 6 \log {\relax (x )} - \frac {2 e^{\frac {5}{2}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________