Optimal. Leaf size=22 \[ e^4 \text {Ei}(-4+2 x)-e^2 \text {Ei}(-2+2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2300, 2209}
\begin {gather*} e^4 \text {ExpIntegralEi}(2 x-4)-e^2 \text {ExpIntegralEi}(2 x-2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rule 2300
Rubi steps
\begin {align*} \int \frac {e^{2 x}}{2-3 x+x^2} \, dx &=\int \left (-\frac {2 e^{2 x}}{4-2 x}-\frac {2 e^{2 x}}{-2+2 x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{2 x}}{4-2 x} \, dx\right )-2 \int \frac {e^{2 x}}{-2+2 x} \, dx\\ &=e^4 \text {Ei}(-4+2 x)-e^2 \text {Ei}(-2+2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 22, normalized size = 1.00 \begin {gather*} e^4 \text {Ei}(-4+2 x)-e^2 \text {Ei}(-2+2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 23, normalized size = 1.05
method | result | size |
derivativedivides | \(-{\mathrm e}^{4} \expIntegral \left (1, -2 x +4\right )+{\mathrm e}^{2} \expIntegral \left (1, -2 x +2\right )\) | \(23\) |
default | \(-{\mathrm e}^{4} \expIntegral \left (1, -2 x +4\right )+{\mathrm e}^{2} \expIntegral \left (1, -2 x +2\right )\) | \(23\) |
risch | \(-{\mathrm e}^{4} \expIntegral \left (1, -2 x +4\right )+{\mathrm e}^{2} \expIntegral \left (1, -2 x +2\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.58, size = 20, normalized size = 0.91 \begin {gather*} {\rm Ei}\left (2 \, x - 4\right ) e^{4} - {\rm Ei}\left (2 \, x - 2\right ) e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{2 x}}{\left (x - 2\right ) \left (x - 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.48, size = 20, normalized size = 0.91 \begin {gather*} {\rm Ei}\left (2 \, x - 4\right ) e^{4} - {\rm Ei}\left (2 \, x - 2\right ) e^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x}}{x^2-3\,x+2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________