Integrand size = 16, antiderivative size = 16 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\text {Int}\left (\frac {\operatorname {FresnelS}(a+b x)^2}{c+d x},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx \]
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Not integrable
Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {FresnelS}\left (b x +a \right )^{2}}{d x +c}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int \frac {S^{2}\left (a + b x\right )}{c + d x}\, dx \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
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Not integrable
Time = 4.88 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\operatorname {FresnelS}(a+b x)^2}{c+d x} \, dx=\int \frac {{\mathrm {FresnelS}\left (a+b\,x\right )}^2}{c+d\,x} \,d x \]
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