3.1552 \(\int (a+\frac{b}{x}) \, dx\)

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

[Out]

a*x + b*Log[x]

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Rubi [A]  time = 0.0019793, 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., Rules used = {} \[ a x+b \log (x) \]

Antiderivative was successfully verified.

[In]

Int[a + b/x,x]

[Out]

a*x + b*Log[x]

Rubi steps

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

Mathematica [A]  time = 0.0006521, 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 \begin{align*} ax+b\ln \left ( x \right ) \end{align*}

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 = 0.969575, size = 11, normalized size = 1.38 \begin{align*} a x + b \log \left (x\right ) \end{align*}

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 = 1.49705, size = 22, normalized size = 2.75 \begin{align*} a x + b \log \left (x\right ) \end{align*}

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 = 0.076756, size = 7, normalized size = 0.88 \begin{align*} a x + b \log{\left (x \right )} \end{align*}

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 [A]  time = 1.17525, size = 12, normalized size = 1.5 \begin{align*} a x + b \log \left ({\left | x \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x,x, algorithm="giac")

[Out]

a*x + b*log(abs(x))