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

Optimal. Leaf size=11 \[ \text {Int}\left (F\left (\frac {a}{x}+b\right ),x\right ) \]

[Out]

CannotIntegrate(F(a/x+b),x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int F\left (\frac {a+b x}{x}\right ) \, dx \]

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*}

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Mathematica [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int F\left (\frac {a+b x}{x}\right ) \, dx \]

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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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (\frac {b x + a}{x}\right ), x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {b x + a}{x}\right )\,{d x} \]

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)

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maple [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int F \left (\frac {b x +a}{x}\right )\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (\frac {b x + a}{x}\right )\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.09 \[ \int F\left (\frac {a+b\,x}{x}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F((a + b*x)/x),x)

[Out]

int(F((a + b*x)/x), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F{\left (\frac {a + b x}{x} \right )}\, dx \]

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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