3.1530 \(\int \frac{1}{2+b x} \, dx\)

Optimal. Leaf size=10 \[ \frac{\log (b x+2)}{b} \]

[Out]

Log[2 + b*x]/b

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Rubi [A]  time = 0.00650141, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{\log (b x+2)}{b} \]

Antiderivative was successfully verified.

[In]  Int[(2 + b*x)^(-1),x]

[Out]

Log[2 + b*x]/b

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Rubi in Sympy [A]  time = 1.35383, size = 7, normalized size = 0.7 \[ \frac{\log{\left (b x + 2 \right )}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b*x+2),x)

[Out]

log(b*x + 2)/b

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Mathematica [A]  time = 0.00126105, size = 10, normalized size = 1. \[ \frac{\log (b x+2)}{b} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + b*x)^(-1),x]

[Out]

Log[2 + b*x]/b

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Maple [A]  time = 0.002, size = 11, normalized size = 1.1 \[{\frac{\ln \left ( bx+2 \right ) }{b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x+2),x)

[Out]

ln(b*x+2)/b

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Maxima [A]  time = 1.38989, size = 14, normalized size = 1.4 \[ \frac{\log \left (b x + 2\right )}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x + 2),x, algorithm="maxima")

[Out]

log(b*x + 2)/b

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Fricas [A]  time = 0.211517, size = 14, normalized size = 1.4 \[ \frac{\log \left (b x + 2\right )}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x + 2),x, algorithm="fricas")

[Out]

log(b*x + 2)/b

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Sympy [A]  time = 0.033749, size = 7, normalized size = 0.7 \[ \frac{\log{\left (b x + 2 \right )}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x+2),x)

[Out]

log(b*x + 2)/b

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GIAC/XCAS [A]  time = 0.214762, size = 15, normalized size = 1.5 \[ \frac{{\rm ln}\left ({\left | b x + 2 \right |}\right )}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x + 2),x, algorithm="giac")

[Out]

ln(abs(b*x + 2))/b