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

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{S(a+b x)}{x^2},x\right ) \]

[Out]

Unintegrable[FresnelS[a + b*x]/x^2, x]

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Rubi [A]  time = 0.0112494, 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 = {} \[ \int \frac{S(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[FresnelS[a + b*x]/x^2,x]

[Out]

Defer[Int][FresnelS[a + b*x]/x^2, x]

Rubi steps

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

Mathematica [A]  time = 3.24649, size = 0, normalized size = 0. \[ \int \frac{S(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[FresnelS[a + b*x]/x^2,x]

[Out]

Integrate[FresnelS[a + b*x]/x^2, x]

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Maple [A]  time = 0.1, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it FresnelS} \left ( bx+a \right ) }{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnels}\left (b x + a\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(fresnels(b*x + a)/x^2, x)

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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 )}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(fresnels(b*x + a)/x^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{S\left (a + b x\right )}{x^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(fresnels(a + b*x)/x**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm fresnels}\left (b x + a\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(fresnels(b*x + a)/x^2, x)