3.2169 \(\int \frac{9+6 x+x^2}{x^2} \, dx\)

Optimal. Leaf size=11 \[ x-\frac{9}{x}+6 \log (x) \]

[Out]

-9/x + x + 6*Log[x]

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Rubi [A]  time = 0.0142194, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ x-\frac{9}{x}+6 \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(9 + 6*x + x^2)/x^2,x]

[Out]

-9/x + x + 6*Log[x]

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Rubi in Sympy [A]  time = 3.91326, size = 8, normalized size = 0.73 \[ x + 6 \log{\left (x \right )} - \frac{9}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2+6*x+9)/x**2,x)

[Out]

x + 6*log(x) - 9/x

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Mathematica [A]  time = 0.00181462, size = 11, normalized size = 1. \[ x-\frac{9}{x}+6 \log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[(9 + 6*x + x^2)/x^2,x]

[Out]

-9/x + x + 6*Log[x]

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Maple [A]  time = 0.008, size = 12, normalized size = 1.1 \[ -9\,{x}^{-1}+x+6\,\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2+6*x+9)/x^2,x)

[Out]

-9/x+x+6*ln(x)

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Maxima [A]  time = 0.793471, size = 15, normalized size = 1.36 \[ x - \frac{9}{x} + 6 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 6*x + 9)/x^2,x, algorithm="maxima")

[Out]

x - 9/x + 6*log(x)

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Fricas [A]  time = 0.220625, size = 19, normalized size = 1.73 \[ \frac{x^{2} + 6 \, x \log \left (x\right ) - 9}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 6*x + 9)/x^2,x, algorithm="fricas")

[Out]

(x^2 + 6*x*log(x) - 9)/x

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Sympy [A]  time = 0.13518, size = 8, normalized size = 0.73 \[ x + 6 \log{\left (x \right )} - \frac{9}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2+6*x+9)/x**2,x)

[Out]

x + 6*log(x) - 9/x

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GIAC/XCAS [A]  time = 0.204514, size = 16, normalized size = 1.45 \[ x - \frac{9}{x} + 6 \,{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 6*x + 9)/x^2,x, algorithm="giac")

[Out]

x - 9/x + 6*ln(abs(x))