Optimal. Leaf size=22 \[ e^4 \text {Ei}(2 x-4)-e^2 \text {Ei}(2 x-2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, 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 = {2268, 2178} \[ e^4 \text {ExpIntegralEi}(2 x-4)-e^2 \text {ExpIntegralEi}(2 x-2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2178
Rule 2268
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 = 0.04, size = 22, normalized size = 1.00 \[ e^4 \text {Ei}(2 x-4)-e^2 \text {Ei}(2 x-2) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 20, normalized size = 0.91 \[ {\rm Ei}\left (2 \, x - 4\right ) e^{4} - {\rm Ei}\left (2 \, x - 2\right ) e^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.01, size = 20, normalized size = 0.91 \[ {\rm Ei}\left (2 \, x - 4\right ) e^{4} - {\rm Ei}\left (2 \, x - 2\right ) e^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 23, normalized size = 1.05 \[ -{\mathrm e}^{4} \Ei \left (1, -2 x +4\right )+{\mathrm e}^{2} \Ei \left (1, -2 x +2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{\left (2 \, x\right )}}{x^{2} - 3 \, x + 2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {e}}^{2\,x}}{x^2-3\,x+2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^{2 x}}{\left (x - 2\right ) \left (x - 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________