Optimal. Leaf size=25 \[ \frac {1}{5} \left (5+e^x+x+\frac {-1+e^5+2 x+x^2}{x^2}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.36, number of steps used = 6, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14, 2194} \begin {gather*} -\frac {1-e^5}{5 x^2}+\frac {x}{5}+\frac {e^x}{5}+\frac {2}{5 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {2-2 e^5-2 x+x^3+e^x x^3}{x^3} \, dx\\ &=\frac {1}{5} \int \left (e^x+\frac {2 \left (1-e^5\right )-2 x+x^3}{x^3}\right ) \, dx\\ &=\frac {\int e^x \, dx}{5}+\frac {1}{5} \int \frac {2 \left (1-e^5\right )-2 x+x^3}{x^3} \, dx\\ &=\frac {e^x}{5}+\frac {1}{5} \int \left (1-\frac {2 \left (-1+e^5\right )}{x^3}-\frac {2}{x^2}\right ) \, dx\\ &=\frac {e^x}{5}-\frac {1-e^5}{5 x^2}+\frac {2}{5 x}+\frac {x}{5}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 26, normalized size = 1.04 \begin {gather*} \frac {1}{5} \left (e^x-\frac {1}{x^2}+\frac {e^5}{x^2}+\frac {2}{x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.71, size = 21, normalized size = 0.84 \begin {gather*} \frac {x^{3} + x^{2} e^{x} + 2 \, x + e^{5} - 1}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 21, normalized size = 0.84 \begin {gather*} \frac {x^{3} + x^{2} e^{x} + 2 \, x + e^{5} - 1}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 21, normalized size = 0.84
method | result | size |
risch | \(\frac {x}{5}+\frac {2 x +{\mathrm e}^{5}-1}{5 x^{2}}+\frac {{\mathrm e}^{x}}{5}\) | \(21\) |
default | \(\frac {x}{5}-\frac {1}{5 x^{2}}+\frac {2}{5 x}+\frac {{\mathrm e}^{5}}{5 x^{2}}+\frac {{\mathrm e}^{x}}{5}\) | \(26\) |
norman | \(\frac {\frac {2 x}{5}+\frac {x^{3}}{5}+\frac {{\mathrm e}^{x} x^{2}}{5}+\frac {{\mathrm e}^{5}}{5}-\frac {1}{5}}{x^{2}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 25, normalized size = 1.00 \begin {gather*} \frac {1}{5} \, x + \frac {2}{5 \, x} + \frac {e^{5}}{5 \, x^{2}} - \frac {1}{5 \, x^{2}} + \frac {1}{5} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.59, size = 21, normalized size = 0.84 \begin {gather*} \frac {x}{5}+\frac {{\mathrm {e}}^x}{5}+\frac {\frac {2\,x}{5}+\frac {{\mathrm {e}}^5}{5}-\frac {1}{5}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 20, normalized size = 0.80 \begin {gather*} \frac {x}{5} + \frac {e^{x}}{5} + \frac {2 x - 1 + e^{5}}{5 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________