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

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

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^3}{3}+x^2+\log (x) \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {x^3}{3}+x^2+\log (x) \end {gather*}

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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (\frac {1}{x}+2 x+x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[x^(-1) + 2*x + x^2,x]

[Out]

IntegrateAlgebraic[x^(-1) + 2*x + x^2, x]

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fricas [A]  time = 1.29, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \relax (x) \end {gather*}

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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giac [A]  time = 1.01, size = 12, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \left ({\left | x \right |}\right ) \end {gather*}

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))

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maple [A]  time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} \frac {x^{3}}{3}+x^{2}+\ln \relax (x ) \end {gather*}

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 = 1.08, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, x^{3} + x^{2} + \log \relax (x) \end {gather*}

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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mupad [B]  time = 0.03, size = 11, normalized size = 0.85 \begin {gather*} \ln \relax (x)+x^2+\frac {x^3}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 1/x + x^2,x)

[Out]

log(x) + x^2 + x^3/3

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sympy [A]  time = 0.08, size = 10, normalized size = 0.77 \begin {gather*} \frac {x^{3}}{3} + x^{2} + \log {\relax (x )} \end {gather*}

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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