Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{S(a+b x)^2}{c+d x},x\right ) \]
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Rubi [A] time = 0.0232799, 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 = {} \[ \int \frac{S(a+b x)^2}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{S(a+b x)^2}{c+d x} \, dx &=\int \frac{S(a+b x)^2}{c+d x} \, dx\\ \end{align*}
Mathematica [A] time = 0.0357935, size = 0, normalized size = 0. \[ \int \frac{S(a+b x)^2}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.36, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it FresnelS} \left ( bx+a \right ) \right ) ^{2}}{dx+c}}\, 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{{\rm fresnels}\left (b x + a\right )^{2}}{d x + c}\,{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{{\rm fresnels}\left (b x + a\right )^{2}}{d x + c}, 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{S^{2}\left (a + b x\right )}{c + d x}\, 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{{\rm fresnels}\left (b x + a\right )^{2}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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