3.56 \(\int \frac{1}{2+3 x} \, dx\)

Optimal. Leaf size=10 \[ \frac{1}{3} \log (3 x+2) \]

[Out]

Log[2 + 3*x]/3

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Rubi [A]  time = 0.00471719, 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 \[ \frac{1}{3} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^(-1),x]

[Out]

Log[2 + 3*x]/3

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Rubi in Sympy [A]  time = 0.509688, size = 7, normalized size = 0.7 \[ \frac{\log{\left (3 x + 2 \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(2+3*x),x)

[Out]

log(3*x + 2)/3

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Mathematica [A]  time = 0.00111162, size = 10, normalized size = 1. \[ \frac{1}{3} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^(-1),x]

[Out]

Log[2 + 3*x]/3

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Maple [A]  time = 0., size = 9, normalized size = 0.9 \[{\frac{\ln \left ( 2+3\,x \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(2+3*x),x)

[Out]

1/3*ln(2+3*x)

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Maxima [A]  time = 1.44508, size = 11, normalized size = 1.1 \[ \frac{1}{3} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(3*x + 2),x, algorithm="maxima")

[Out]

1/3*log(3*x + 2)

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Fricas [A]  time = 0.203973, size = 11, normalized size = 1.1 \[ \frac{1}{3} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(3*x + 2),x, algorithm="fricas")

[Out]

1/3*log(3*x + 2)

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Sympy [A]  time = 0.031041, size = 7, normalized size = 0.7 \[ \frac{\log{\left (3 x + 2 \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(2+3*x),x)

[Out]

log(3*x + 2)/3

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GIAC/XCAS [A]  time = 0.21534, size = 12, normalized size = 1.2 \[ \frac{1}{3} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(3*x + 2),x, algorithm="giac")

[Out]

1/3*ln(abs(3*x + 2))