3.163 \(\int \frac{7}{-12+5 x+2 x^2} \, dx\)

Optimal. Leaf size=19 \[ \frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (x+4) \]

[Out]

(7*Log[3 - 2*x])/11 - (7*Log[4 + x])/11

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Rubi [A]  time = 0.0137621, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{7}{11} \log (3-2 x)-\frac{7}{11} \log (x+4) \]

Antiderivative was successfully verified.

[In]  Int[7/(-12 + 5*x + 2*x^2),x]

[Out]

(7*Log[3 - 2*x])/11 - (7*Log[4 + x])/11

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Rubi in Sympy [A]  time = 1.52941, size = 17, normalized size = 0.89 \[ \frac{7 \log{\left (- 2 x + 3 \right )}}{11} - \frac{7 \log{\left (x + 4 \right )}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(7/(2*x**2+5*x-12),x)

[Out]

7*log(-2*x + 3)/11 - 7*log(x + 4)/11

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Mathematica [A]  time = 0.00472871, size = 21, normalized size = 1.11 \[ 7 \left (\frac{1}{11} \log (3-2 x)-\frac{1}{11} \log (x+4)\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[7/(-12 + 5*x + 2*x^2),x]

[Out]

7*(Log[3 - 2*x]/11 - Log[4 + x]/11)

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Maple [A]  time = 0.009, size = 16, normalized size = 0.8 \[ -{\frac{7\,\ln \left ( 4+x \right ) }{11}}+{\frac{7\,\ln \left ( -3+2\,x \right ) }{11}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(7/(2*x^2+5*x-12),x)

[Out]

-7/11*ln(4+x)+7/11*ln(-3+2*x)

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Maxima [A]  time = 1.34806, size = 20, normalized size = 1.05 \[ \frac{7}{11} \, \log \left (2 \, x - 3\right ) - \frac{7}{11} \, \log \left (x + 4\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(7/(2*x^2 + 5*x - 12),x, algorithm="maxima")

[Out]

7/11*log(2*x - 3) - 7/11*log(x + 4)

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Fricas [A]  time = 0.199643, size = 20, normalized size = 1.05 \[ \frac{7}{11} \, \log \left (2 \, x - 3\right ) - \frac{7}{11} \, \log \left (x + 4\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(7/(2*x^2 + 5*x - 12),x, algorithm="fricas")

[Out]

7/11*log(2*x - 3) - 7/11*log(x + 4)

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Sympy [A]  time = 0.091085, size = 17, normalized size = 0.89 \[ \frac{7 \log{\left (x - \frac{3}{2} \right )}}{11} - \frac{7 \log{\left (x + 4 \right )}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(7/(2*x**2+5*x-12),x)

[Out]

7*log(x - 3/2)/11 - 7*log(x + 4)/11

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GIAC/XCAS [A]  time = 0.204714, size = 23, normalized size = 1.21 \[ \frac{7}{11} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) - \frac{7}{11} \,{\rm ln}\left ({\left | x + 4 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(7/(2*x^2 + 5*x - 12),x, algorithm="giac")

[Out]

7/11*ln(abs(2*x - 3)) - 7/11*ln(abs(x + 4))