3.1909 \(\int \left (\frac{1}{x}+2 x+x^2\right ) \, dx\)

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

[Out]

x^2 + x^3/3 + Log[x]

_______________________________________________________________________________________

Rubi [A]  time = 0.00654493, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{x^3}{3}+x^2+\log (x) \]

Antiderivative was successfully verified.

[In]  Int[x^(-1) + 2*x + x^2,x]

[Out]

x^2 + x^3/3 + Log[x]

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x+2*x+x**2,x)

[Out]

x**3/3 + log(x) + 2*Integral(x, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00144664, size = 13, normalized size = 1. \[ \frac{x^3}{3}+x^2+\log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-1) + 2*x + x^2,x]

[Out]

x^2 + x^3/3 + Log[x]

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 12, normalized size = 0.9 \[{x}^{2}+{\frac{{x}^{3}}{3}}+\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x+2*x+x^2,x)

[Out]

x^2+1/3*x^3+ln(x)

_______________________________________________________________________________________

Maxima [A]  time = 1.36116, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2 + 2*x + 1/x,x, algorithm="maxima")

[Out]

1/3*x^3 + x^2 + log(x)

_______________________________________________________________________________________

Fricas [A]  time = 0.197987, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2 + 2*x + 1/x,x, algorithm="fricas")

[Out]

1/3*x^3 + x^2 + log(x)

_______________________________________________________________________________________

Sympy [A]  time = 0.063826, size = 10, normalized size = 0.77 \[ \frac{x^{3}}{3} + x^{2} + \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x+2*x+x**2,x)

[Out]

x**3/3 + x**2 + log(x)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.271008, size = 16, normalized size = 1.23 \[ \frac{1}{3} \, x^{3} + x^{2} +{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2 + 2*x + 1/x,x, algorithm="giac")

[Out]

1/3*x^3 + x^2 + ln(abs(x))