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

Optimal. Leaf size=13 \[ \text {Int}\left (F\left (\frac {x}{a+b x}\right ),x\right ) \]

[Out]

CannotIntegrate(F(x/(b*x+a)),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 = {} \[ \int F\left (\frac {x}{a+b x}\right ) \, dx \]

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*}

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

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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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (\frac {x}{b x + a}\right ), x\right ) \]

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

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)

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

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

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int F\left (\frac {x}{a+b\,x}\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x/(a + b*x)),x)

[Out]

int(F(x/(a + b*x)), x)

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

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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