3.180 \(\int \frac{-5+6 x}{3+2 x} \, dx\)

Optimal. Leaf size=12 \[ 3 x-7 \log (2 x+3) \]

[Out]

3*x - 7*Log[3 + 2*x]

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Rubi [A]  time = 0.0157124, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ 3 x-7 \log (2 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(-5 + 6*x)/(3 + 2*x),x]

[Out]

3*x - 7*Log[3 + 2*x]

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Rubi in Sympy [A]  time = 1.61684, size = 10, normalized size = 0.83 \[ 3 x - 7 \log{\left (2 x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-5+6*x)/(3+2*x),x)

[Out]

3*x - 7*log(2*x + 3)

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Mathematica [A]  time = 0.00435113, size = 15, normalized size = 1.25 \[ 3 x-7 \log (2 x+3)+\frac{9}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[(-5 + 6*x)/(3 + 2*x),x]

[Out]

9/2 + 3*x - 7*Log[3 + 2*x]

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Maple [A]  time = 0.003, size = 13, normalized size = 1.1 \[ 3\,x-7\,\ln \left ( 3+2\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-5+6*x)/(3+2*x),x)

[Out]

3*x-7*ln(3+2*x)

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Maxima [A]  time = 1.41085, size = 16, normalized size = 1.33 \[ 3 \, x - 7 \, \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 5)/(2*x + 3),x, algorithm="maxima")

[Out]

3*x - 7*log(2*x + 3)

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Fricas [A]  time = 0.189837, size = 16, normalized size = 1.33 \[ 3 \, x - 7 \, \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 5)/(2*x + 3),x, algorithm="fricas")

[Out]

3*x - 7*log(2*x + 3)

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Sympy [A]  time = 0.060313, size = 10, normalized size = 0.83 \[ 3 x - 7 \log{\left (2 x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-5+6*x)/(3+2*x),x)

[Out]

3*x - 7*log(2*x + 3)

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GIAC/XCAS [A]  time = 0.207369, size = 18, normalized size = 1.5 \[ 3 \, x - 7 \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((6*x - 5)/(2*x + 3),x, algorithm="giac")

[Out]

3*x - 7*ln(abs(2*x + 3))