Optimal. Leaf size=21 \[ 4-e^{3-4 x}+\frac {3}{x}-\frac {x}{2} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 6, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {12, 14, 2194} \begin {gather*} -\frac {x}{2}-e^{3-4 x}+\frac {3}{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}{2} \int \frac {-6-x^2+8 e^{3-4 x} x^2}{x^2} \, dx\\ &=\frac {1}{2} \int \left (8 e^{3-4 x}+\frac {-6-x^2}{x^2}\right ) \, dx\\ &=\frac {1}{2} \int \frac {-6-x^2}{x^2} \, dx+4 \int e^{3-4 x} \, dx\\ &=-e^{3-4 x}+\frac {1}{2} \int \left (-1-\frac {6}{x^2}\right ) \, dx\\ &=-e^{3-4 x}+\frac {3}{x}-\frac {x}{2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 20, normalized size = 0.95 \begin {gather*} -e^{3-4 x}+\frac {3}{x}-\frac {x}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.12, size = 19, normalized size = 0.90 \begin {gather*} -\frac {x^{2} + 2 \, x e^{\left (-4 \, x + 3\right )} - 6}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.13, size = 19, normalized size = 0.90 \begin {gather*} -\frac {x^{2} + 2 \, x e^{\left (-4 \, x + 3\right )} - 6}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.14, size = 18, normalized size = 0.86
method | result | size |
risch | \(-\frac {x}{2}+\frac {3}{x}-{\mathrm e}^{3-4 x}\) | \(18\) |
derivativedivides | \(\frac {3}{x}+\frac {3}{8}-\frac {x}{2}-{\mathrm e}^{3-4 x}\) | \(19\) |
default | \(\frac {3}{x}+\frac {3}{8}-\frac {x}{2}-{\mathrm e}^{3-4 x}\) | \(19\) |
norman | \(\frac {3-\frac {x^{2}}{2}-x \,{\mathrm e}^{3-4 x}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{2} \, x + \frac {3}{x} - e^{\left (-4 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.03, size = 17, normalized size = 0.81 \begin {gather*} \frac {3}{x}-{\mathrm {e}}^{3-4\,x}-\frac {x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 12, normalized size = 0.57 \begin {gather*} - \frac {x}{2} - e^{3 - 4 x} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________