3.1550 \(\int \left (a+\frac{b}{x}\right ) \, dx\)

Optimal. Leaf size=8 \[ a x+b \log (x) \]

[Out]

a*x + b*Log[x]

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Rubi [A]  time = 0.00910128, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+b \log (x) \]

Antiderivative was successfully verified.

[In]  Int[a + b/x,x]

[Out]

a*x + b*Log[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ b \log{\left (x \right )} + \int a\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(a+b/x,x)

[Out]

b*log(x) + Integral(a, x)

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Mathematica [A]  time = 0.00145592, size = 8, normalized size = 1. \[ a x+b \log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[a + b/x,x]

[Out]

a*x + b*Log[x]

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Maple [A]  time = 0.002, size = 9, normalized size = 1.1 \[ ax+b\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(a+b/x,x)

[Out]

a*x+b*ln(x)

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Maxima [A]  time = 1.41533, size = 11, normalized size = 1.38 \[ a x + b \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x,x, algorithm="maxima")

[Out]

a*x + b*log(x)

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Fricas [A]  time = 0.222659, size = 11, normalized size = 1.38 \[ a x + b \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x,x, algorithm="fricas")

[Out]

a*x + b*log(x)

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Sympy [A]  time = 0.145719, size = 7, normalized size = 0.88 \[ a x + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a+b/x,x)

[Out]

a*x + b*log(x)

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GIAC/XCAS [A]  time = 0.225704, size = 12, normalized size = 1.5 \[ a x + b{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x,x, algorithm="giac")

[Out]

a*x + b*ln(abs(x))