3.60 \(\int \frac{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx\)

Optimal. Leaf size=25 \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]

[Out]

Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]/8

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Rubi [A]  time = 0.0121434, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026 \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 3*x + 30*x^2 + 160*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]

[Out]

Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]/8

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Rubi in Sympy [A]  time = 3.60071, size = 22, normalized size = 0.88 \[ \frac{\log{\left (320 x^{4} + 80 x^{3} - 12 x^{2} + 24 x + 9 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((160*x**3+30*x**2-3*x+3)/(320*x**4+80*x**3-12*x**2+24*x+9),x)

[Out]

log(320*x**4 + 80*x**3 - 12*x**2 + 24*x + 9)/8

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Mathematica [A]  time = 0.0117437, size = 25, normalized size = 1. \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - 3*x + 30*x^2 + 160*x^3)/(9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4),x]

[Out]

Log[9 + 24*x - 12*x^2 + 80*x^3 + 320*x^4]/8

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Maple [A]  time = 0.001, size = 24, normalized size = 1. \[{\frac{\ln \left ( 320\,{x}^{4}+80\,{x}^{3}-12\,{x}^{2}+24\,x+9 \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((160*x^3+30*x^2-3*x+3)/(320*x^4+80*x^3-12*x^2+24*x+9),x)

[Out]

1/8*ln(320*x^4+80*x^3-12*x^2+24*x+9)

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Maxima [A]  time = 1.38999, size = 31, normalized size = 1.24 \[ \frac{1}{8} \, \log \left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((160*x^3 + 30*x^2 - 3*x + 3)/(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9),x, algorithm="maxima")

[Out]

1/8*log(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9)

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Fricas [A]  time = 0.194498, size = 31, normalized size = 1.24 \[ \frac{1}{8} \, \log \left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((160*x^3 + 30*x^2 - 3*x + 3)/(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9),x, algorithm="fricas")

[Out]

1/8*log(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9)

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Sympy [A]  time = 0.107169, size = 22, normalized size = 0.88 \[ \frac{\log{\left (320 x^{4} + 80 x^{3} - 12 x^{2} + 24 x + 9 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((160*x**3+30*x**2-3*x+3)/(320*x**4+80*x**3-12*x**2+24*x+9),x)

[Out]

log(320*x**4 + 80*x**3 - 12*x**2 + 24*x + 9)/8

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GIAC/XCAS [A]  time = 0.244751, size = 31, normalized size = 1.24 \[ \frac{1}{8} \,{\rm ln}\left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((160*x^3 + 30*x^2 - 3*x + 3)/(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9),x, algorithm="giac")

[Out]

1/8*ln(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9)