Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\text{Erf}(a+b x)^2}{(c+d x)^2},x\right ) \]
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Rubi [A] time = 0.0222502, 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 = {} \[ \int \frac{\text{Erf}(a+b x)^2}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{erf}(a+b x)^2}{(c+d x)^2} \, dx &=\int \frac{\text{erf}(a+b x)^2}{(c+d x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.105703, size = 0, normalized size = 0. \[ \int \frac{\text{Erf}(a+b x)^2}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.365, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it Erf} \left ( bx+a \right ) \right ) ^{2}}{ \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*} 4 \, b \int \frac{\operatorname{erf}\left (b x + a\right ) e^{\left (-b^{2} x^{2} - 2 \, a b x\right )}}{\sqrt{\pi } d^{2} x e^{\left (a^{2}\right )} + \sqrt{\pi } c d e^{\left (a^{2}\right )}}\,{d x} - \frac{\operatorname{erf}\left (b x + a\right )^{2}}{d^{2} x + c d} \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 )^{2}}{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{erf}^{2}{\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{erf}\left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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