Optimal. Leaf size=17 \[ 10-\frac {e^x}{5 x}+x+\log \left (\frac {14}{3}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 12, normalized size of antiderivative = 0.71, number of steps used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2197} \begin {gather*} x-\frac {e^x}{5 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {e^x (1-x)+5 x^2}{x^2} \, dx\\ &=\frac {1}{5} \int \left (5-\frac {e^x (-1+x)}{x^2}\right ) \, dx\\ &=x-\frac {1}{5} \int \frac {e^x (-1+x)}{x^2} \, dx\\ &=-\frac {e^x}{5 x}+x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 12, normalized size = 0.71 \begin {gather*} -\frac {e^x}{5 x}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.57, size = 15, normalized size = 0.88 \begin {gather*} \frac {5 \, x^{2} - e^{x}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 15, normalized size = 0.88 \begin {gather*} \frac {5 \, x^{2} - e^{x}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 10, normalized size = 0.59
method | result | size |
default | \(x -\frac {{\mathrm e}^{x}}{5 x}\) | \(10\) |
risch | \(x -\frac {{\mathrm e}^{x}}{5 x}\) | \(10\) |
norman | \(\frac {x^{2}-\frac {{\mathrm e}^{x}}{5}}{x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [C] time = 0.38, size = 13, normalized size = 0.76 \begin {gather*} x - \frac {1}{5} \, {\rm Ei}\relax (x) + \frac {1}{5} \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 9, normalized size = 0.53 \begin {gather*} x-\frac {{\mathrm {e}}^x}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 7, normalized size = 0.41 \begin {gather*} x - \frac {e^{x}}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________