Integrand size = 14, antiderivative size = 14 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\text {Int}\left (\frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx \\ \end{align*}
Not integrable
Time = 2.30 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {FresnelS}\left (b x +a \right )}{\left (d x +c \right )^{2}}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.93 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.58 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int \frac {S\left (a + b x\right )}{\left (c + d x\right )^{2}}\, dx \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int { \frac {\operatorname {S}\left (b x + a\right )}{{\left (d x + c\right )}^{2}} \,d x } \]
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Not integrable
Time = 4.82 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {\operatorname {FresnelS}(a+b x)}{(c+d x)^2} \, dx=\int \frac {\mathrm {FresnelS}\left (a+b\,x\right )}{{\left (c+d\,x\right )}^2} \,d x \]
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