3.907 \(\int F(\frac{x}{a+b x}) \, dx\)

Optimal. Leaf size=12 \[ \text{CannotIntegrate}\left (F\left (\frac{x}{a+b x}\right ),x\right ) \]

[Out]

CannotIntegrate[F[x/(a + b*x)], x]

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Rubi [A]  time = 0.0078925, 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 = {} \[ \int F\left (\frac{x}{a+b x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[x/(a + b*x)],x]

[Out]

Defer[Int][F[x/(a + b*x)], x]

Rubi steps

\begin{align*} \int F\left (\frac{x}{a+b x}\right ) \, dx &=\int F\left (\frac{x}{a+b x}\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 0.0056554, size = 0, normalized size = 0. \[ \int F\left (\frac{x}{a+b x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[x/(a + b*x)],x]

[Out]

Integrate[F[x/(a + b*x)], x]

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Maple [A]  time = 0.007, size = 0, normalized size = 0. \begin{align*} \int F \left ({\frac{x}{bx+a}} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x/(b*x+a)),x)

[Out]

int(F(x/(b*x+a)),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x/(b*x+a)),x, algorithm="maxima")

[Out]

integrate(F(x/(b*x + a)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (F\left (\frac{x}{b x + a}\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x/(b*x+a)),x, algorithm="fricas")

[Out]

integral(F(x/(b*x + a)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x/(b*x+a)),x)

[Out]

Integral(F(x/(a + b*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x/(b*x+a)),x, algorithm="giac")

[Out]

integrate(F(x/(b*x + a)), x)