3.1.52 \(\int \frac {S(a+b x)^2}{c+d x} \, dx\) [52]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {S(a+b x)^2}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {S(a+b x)^2}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[FresnelS[a + b*x]^2/(c + d*x),x]

[Out]

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

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*}

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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {S(a+b x)^2}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.24, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {S}\left (b x +a \right )^{2}}{d x +c}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {S^{2}\left (a + b x\right )}{c + d x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {FresnelS}\left (a+b\,x\right )}^2}{c+d\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(FresnelS(a + b*x)^2/(c + d*x),x)

[Out]

int(FresnelS(a + b*x)^2/(c + d*x), x)

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