3.478 \(\int \frac{-7+4 x^2}{3+2 x} \, dx\)

Optimal. Leaf size=13 \[ x^2-3 x+\log (2 x+3) \]

[Out]

-3*x + x^2 + Log[3 + 2*x]

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Rubi [A]  time = 0.026308, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ x^2-3 x+\log (2 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(-7 + 4*x^2)/(3 + 2*x),x]

[Out]

-3*x + x^2 + Log[3 + 2*x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 3 x + \log{\left (2 x + 3 \right )} + 2 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((4*x**2-7)/(3+2*x),x)

[Out]

-3*x + log(2*x + 3) + 2*Integral(x, x)

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Mathematica [A]  time = 0.00589985, size = 16, normalized size = 1.23 \[ x^2-3 x+\log (2 x+3)-\frac{27}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[(-7 + 4*x^2)/(3 + 2*x),x]

[Out]

-27/4 - 3*x + x^2 + Log[3 + 2*x]

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Maple [A]  time = 0.003, size = 14, normalized size = 1.1 \[ -3\,x+{x}^{2}+\ln \left ( 3+2\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((4*x^2-7)/(3+2*x),x)

[Out]

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

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Maxima [A]  time = 0.782027, size = 18, normalized size = 1.38 \[ x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)/(2*x + 3),x, algorithm="maxima")

[Out]

x^2 - 3*x + log(2*x + 3)

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Fricas [A]  time = 0.261004, size = 18, normalized size = 1.38 \[ x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)/(2*x + 3),x, algorithm="fricas")

[Out]

x^2 - 3*x + log(2*x + 3)

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Sympy [A]  time = 0.123443, size = 12, normalized size = 0.92 \[ x^{2} - 3 x + \log{\left (2 x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x**2-7)/(3+2*x),x)

[Out]

x**2 - 3*x + log(2*x + 3)

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GIAC/XCAS [A]  time = 0.26133, size = 19, normalized size = 1.46 \[ x^{2} - 3 \, x +{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)/(2*x + 3),x, algorithm="giac")

[Out]

x^2 - 3*x + ln(abs(2*x + 3))