3.53 \(\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{S(a+b x)^2}{(c+d x)^2},x\right ) \]

[Out]

Unintegrable[FresnelS[a + b*x]^2/(c + d*x)^2, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0228937, 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 = {} \[ \int \frac{S(a+b x)^2}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[FresnelS[a + b*x]^2/(c + d*x)^2,x]

[Out]

Defer[Int][FresnelS[a + b*x]^2/(c + d*x)^2, x]

Rubi steps

\begin{align*} \int \frac{S(a+b x)^2}{(c+d x)^2} \, dx &=\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0817917, size = 0, normalized size = 0. \[ \int \frac{S(a+b x)^2}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[FresnelS[a + b*x]^2/(c + d*x)^2,x]

[Out]

Integrate[FresnelS[a + b*x]^2/(c + d*x)^2, x]

________________________________________________________________________________________

Maple [A]  time = 0.355, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it FresnelS} \left ( bx+a \right ) \right ) ^{2}}{ \left ( dx+c \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(FresnelS(b*x+a)^2/(d*x+c)^2,x)

[Out]

int(FresnelS(b*x+a)^2/(d*x+c)^2,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnels}\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.

[In]

integrate(fresnels(b*x+a)^2/(d*x+c)^2,x, algorithm="maxima")

[Out]

integrate(fresnels(b*x + a)^2/(d*x + c)^2, x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\rm fresnels}\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.

[In]

integrate(fresnels(b*x+a)^2/(d*x+c)^2,x, algorithm="fricas")

[Out]

integral(fresnels(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{S^{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.

[In]

integrate(fresnels(b*x+a)**2/(d*x+c)**2,x)

[Out]

Integral(fresnels(a + b*x)**2/(c + d*x)**2, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnels}\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.

[In]

integrate(fresnels(b*x+a)^2/(d*x+c)^2,x, algorithm="giac")

[Out]

integrate(fresnels(b*x + a)^2/(d*x + c)^2, x)