Optimal. Leaf size=25 \[ 1+\frac {e^{-1+x}}{-3+e^x}-25 (3-x)-3 x \]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 18, normalized size of antiderivative = 0.72, number of steps used = 4, number of rules used = 3, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {2282, 12, 893} \begin {gather*} 22 x-\frac {3}{e \left (3-e^x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 893
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {198 e-3 (1+44 e) x+22 e x^2}{e (3-x)^2 x} \, dx,x,e^x\right )\\ &=\frac {\operatorname {Subst}\left (\int \frac {198 e-3 (1+44 e) x+22 e x^2}{(3-x)^2 x} \, dx,x,e^x\right )}{e}\\ &=\frac {\operatorname {Subst}\left (\int \left (-\frac {3}{(-3+x)^2}+\frac {22 e}{x}\right ) \, dx,x,e^x\right )}{e}\\ &=-\frac {3}{e \left (3-e^x\right )}+22 x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 20, normalized size = 0.80 \begin {gather*} \frac {-\frac {3}{3-e^x}+22 e x}{e} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 28, normalized size = 1.12 \begin {gather*} \frac {66 \, x e - 22 \, x e^{\left (x + 1\right )} - 3}{3 \, e - e^{\left (x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 14, normalized size = 0.56 \begin {gather*} 22 \, x + \frac {3 \, e^{\left (-1\right )}}{e^{x} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 15, normalized size = 0.60
method | result | size |
risch | \(22 x +\frac {3 \,{\mathrm e}^{-1}}{{\mathrm e}^{x}-3}\) | \(15\) |
derivativedivides | \({\mathrm e}^{-1} \left (\frac {3}{{\mathrm e}^{x}-3}+22 \,{\mathrm e} \ln \left ({\mathrm e}^{x}\right )\right )\) | \(22\) |
default | \({\mathrm e}^{-1} \left (\frac {3}{{\mathrm e}^{x}-3}+22 \,{\mathrm e} \ln \left ({\mathrm e}^{x}\right )\right )\) | \(22\) |
norman | \(\frac {-66 x +22 \,{\mathrm e}^{x} x +3 \,{\mathrm e}^{-1}}{{\mathrm e}^{x}-3}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 19, normalized size = 0.76 \begin {gather*} 22 \, x - \frac {3}{3 \, e - e^{\left (x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.55, size = 17, normalized size = 0.68 \begin {gather*} 22\,x+\frac {3}{{\mathrm {e}}^{x+1}-3\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 15, normalized size = 0.60 \begin {gather*} 22 x + \frac {3}{e e^{x} - 3 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________