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

Optimal. Leaf size=10 \[ \text{CannotIntegrate}\left (F\left (\frac{a}{x}+b\right ),x\right ) \]

[Out]

CannotIntegrate[F[b + a/x], x]

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Rubi [A]  time = 0.0123544, 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 = {} \[ \int F\left (\frac{a+b x}{x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[(a + b*x)/x],x]

[Out]

Defer[Int][F[b + a/x], x]

Rubi steps

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

Mathematica [A]  time = 0.0051797, size = 0, normalized size = 0. \[ \int F\left (\frac{a+b x}{x}\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[(a + b*x)/x],x]

[Out]

Integrate[F[(a + b*x)/x], x]

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Maple [A]  time = 0.013, size = 0, normalized size = 0. \begin{align*} \int F \left ({\frac{bx+a}{x}} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F((b*x + a)/x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(F((b*x + a)/x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(F((a + b*x)/x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F((b*x + a)/x), x)