3.1907 \(\int \left (1+\frac{1}{x}+x\right ) \, dx\)

Optimal. Leaf size=11 \[ \frac{x^2}{2}+x+\log (x) \]

[Out]

x + x^2/2 + Log[x]

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Rubi [A]  time = 0.00543139, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{x^2}{2}+x+\log (x) \]

Antiderivative was successfully verified.

[In]  Int[1 + x^(-1) + x,x]

[Out]

x + x^2/2 + Log[x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1+1/x+x,x)

[Out]

x + log(x) + Integral(x, x)

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Mathematica [A]  time = 0.000926031, size = 11, normalized size = 1. \[ \frac{x^2}{2}+x+\log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[1 + x^(-1) + x,x]

[Out]

x + x^2/2 + Log[x]

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Maple [A]  time = 0.002, size = 10, normalized size = 0.9 \[ x+{\frac{{x}^{2}}{2}}+\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1+1/x+x,x)

[Out]

x+1/2*x^2+ln(x)

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Maxima [A]  time = 1.33625, size = 12, normalized size = 1.09 \[ \frac{1}{2} \, x^{2} + x + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x + 1/x + 1,x, algorithm="maxima")

[Out]

1/2*x^2 + x + log(x)

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Fricas [A]  time = 0.203674, size = 12, normalized size = 1.09 \[ \frac{1}{2} \, x^{2} + x + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x + 1/x + 1,x, algorithm="fricas")

[Out]

1/2*x^2 + x + log(x)

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Sympy [A]  time = 0.059823, size = 8, normalized size = 0.73 \[ \frac{x^{2}}{2} + x + \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1+1/x+x,x)

[Out]

x**2/2 + x + log(x)

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GIAC/XCAS [A]  time = 0.310902, size = 14, normalized size = 1.27 \[ \frac{1}{2} \, x^{2} + x +{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x + 1/x + 1,x, algorithm="giac")

[Out]

1/2*x^2 + x + ln(abs(x))