Optimal. Leaf size=20 \[ 8 x+\frac {-e+3 x-4 x^2}{x} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} 4 x-\frac {e}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4+\frac {e}{x^2}\right ) \, dx\\ &=-\frac {e}{x}+4 x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 10, normalized size = 0.50 \begin {gather*} -\frac {e}{x}+4 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 14, normalized size = 0.70 \begin {gather*} \frac {4 \, x^{2} - e}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 11, normalized size = 0.55 \begin {gather*} 4 \, x - \frac {e}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 12, normalized size = 0.60
method | result | size |
default | \(-\frac {{\mathrm e}}{x}+4 x\) | \(12\) |
risch | \(-\frac {{\mathrm e}}{x}+4 x\) | \(12\) |
gosper | \(-\frac {-4 x^{2}+{\mathrm e}}{x}\) | \(14\) |
norman | \(\frac {4 x^{2}-{\mathrm e}}{x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 11, normalized size = 0.55 \begin {gather*} 4 \, x - \frac {e}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 11, normalized size = 0.55 \begin {gather*} 4\,x-\frac {\mathrm {e}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 7, normalized size = 0.35 \begin {gather*} 4 x - \frac {e}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________