Optimal. Leaf size=51 \[ -\frac{2 b \text{Unintegrable}\left (\frac{e^{-(a+b x)^2}}{c+d x},x\right )}{\sqrt{\pi } d}-\frac{\text{Erfc}(a+b x)}{d (c+d x)} \]
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Rubi [A] time = 0.038967, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\text{Erfc}(a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{erfc}(a+b x)}{(c+d x)^2} \, dx &=-\frac{\text{erfc}(a+b x)}{d (c+d x)}-\frac{(2 b) \int \frac{e^{-(a+b x)^2}}{c+d x} \, dx}{d \sqrt{\pi }}\\ \end{align*}
Mathematica [A] time = 0.488978, size = 0, normalized size = 0. \[ \int \frac{\text{Erfc}(a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.375, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it erfc} \left ( bx+a \right ) }{ \left ( dx+c \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x + a\right )}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\operatorname{erf}\left (b x + a\right ) - 1}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{erfc}\left (b x + a\right )}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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