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

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

[Out]

x^2 + x^3/3 + Log[x]

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Rubi [A]  time = 0.0016842, 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., Rules used = {} \[ \frac{x^3}{3}+x^2+\log (x) \]

Antiderivative was successfully verified.

[In]

Int[x^(-1) + 2*x + x^2,x]

[Out]

x^2 + x^3/3 + Log[x]

Rubi steps

\begin{align*} \int \left (\frac{1}{x}+2 x+x^2\right ) \, dx &=x^2+\frac{x^3}{3}+\log (x)\\ \end{align*}

Mathematica [A]  time = 0.0008609, 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]

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

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)

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Maxima [A]  time = 0.986445, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + x^2 + log(x)

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Fricas [A]  time = 1.97332, size = 32, normalized size = 2.46 \begin{align*} \frac{1}{3} \, x^{3} + x^{2} + \log \left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + x^2 + log(x)

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Sympy [A]  time = 0.073692, size = 10, normalized size = 0.77 \begin{align*} \frac{x^{3}}{3} + x^{2} + \log{\left (x \right )} \end{align*}

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)

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Giac [A]  time = 1.056, size = 16, normalized size = 1.23 \begin{align*} \frac{1}{3} \, x^{3} + x^{2} + \log \left ({\left | x \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + x^2 + log(abs(x))