Optimal. Leaf size=11 \[ \text {Ei}\left (a+b x+c x^2\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {6707, 2178} \[ \text {Ei}\left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
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Rule 2178
Rule 6707
Rubi steps
\begin {align*} \int \frac {e^{a+b x+c x^2} (b+2 c x)}{a+b x+c x^2} \, dx &=\operatorname {Subst}\left (\int \frac {e^x}{x} \, dx,x,a+b x+c x^2\right )\\ &=\text {Ei}\left (a+b x+c x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.02, size = 10, normalized size = 0.91 \[ \text {Ei}(a+x (b+c x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 11, normalized size = 1.00 \[ {\rm Ei}\left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (2 \, c x + b\right )} e^{\left (c x^{2} + b x + a\right )}}{c x^{2} + b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 1.73 \[ -\Ei \left (1, -c \,x^{2}-b x -a \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (2 \, c x + b\right )} e^{\left (c x^{2} + b x + a\right )}}{c x^{2} + b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.79, size = 11, normalized size = 1.00 \[ \mathrm {ei}\left (c\,x^2+b\,x+a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.02, size = 10, normalized size = 0.91 \[ \operatorname {Ei}{\left (a + b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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