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

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

[Out]

a*x+b*ln(x)

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \[ a x+b \log (x) \]

Antiderivative was successfully verified.

[In]

Integrate[a + b/x,x]

[Out]

a*x + b*Log[x]

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fricas [A]  time = 0.85, size = 8, normalized size = 1.00 \[ a x + b \log \relax (x) \]

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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giac [A]  time = 0.17, size = 9, normalized size = 1.12 \[ a x + b \log \left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x,x, algorithm="giac")

[Out]

a*x + b*log(abs(x))

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maple [A]  time = 0.00, size = 9, normalized size = 1.12 \[ a x +b \ln \relax (x ) \]

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 = 0.96, size = 8, normalized size = 1.00 \[ a x + b \log \relax (x) \]

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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mupad [B]  time = 0.02, size = 8, normalized size = 1.00 \[ a\,x+b\,\ln \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b/x,x)

[Out]

a*x + b*log(x)

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sympy [A]  time = 0.09, size = 7, normalized size = 0.88 \[ a x + b \log {\relax (x )} \]

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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