Optimal. Leaf size=11 \[ \text {Ei}\left (a+b x+c x^2\right ) \]
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Rubi [A]
time = 0.12, 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 = {6839, 2209}
\begin {gather*} \text {Ei}\left (a+b x+c x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 6839
Rubi steps
\begin {align*} \int \frac {e^{a+b x+c x^2} (b+2 c x)}{a+b x+c x^2} \, dx &=\text {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 = 0.10, size = 10, normalized size = 0.91 \begin {gather*} \text {Ei}(a+x (b+c x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 19, normalized size = 1.73
method | result | size |
derivativedivides | \(-\expIntegral \left (1, -c \,x^{2}-b x -a \right )\) | \(19\) |
default | \(-\expIntegral \left (1, -c \,x^{2}-b x -a \right )\) | \(19\) |
risch | \(-\expIntegral \left (1, -c \,x^{2}-b x -a \right )\) | \(19\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 11, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (c x^{2} + b x + a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 9.08, size = 10, normalized size = 0.91 \begin {gather*} \operatorname {Ei}{\left (a + b x + c x^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.84, size = 11, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (c x^{2} + b x + a\right ) \end {gather*}
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 \begin {gather*} \mathrm {ei}\left (c\,x^2+b\,x+a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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