3.1 \(\int (1+x+x^2) \, dx\)

Optimal. Leaf size=16 \[ \frac {x^3}{3}+\frac {x^2}{2}+x \]

[Out]

x+1/2*x^2+1/3*x^3

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \frac {x^3}{3}+\frac {x^2}{2}+x \]

Antiderivative was successfully verified.

[In]

Int[1 + x + x^2,x]

[Out]

x + x^2/2 + x^3/3

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.00 \[ \frac {x^3}{3}+\frac {x^2}{2}+x \]

Antiderivative was successfully verified.

[In]

Integrate[1 + x + x^2,x]

[Out]

x + x^2/2 + x^3/3

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fricas [A]  time = 0.39, size = 12, normalized size = 0.75 \[ \frac {1}{3} x^{3} + \frac {1}{2} x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + 1/2*x^2 + x

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giac [A]  time = 1.24, size = 12, normalized size = 0.75 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + 1/2*x^2 + x

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maple [A]  time = 0.00, size = 13, normalized size = 0.81 \[ \frac {1}{3} x^{3}+\frac {1}{2} x^{2}+x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2+x+1,x)

[Out]

x+1/2*x^2+1/3*x^3

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maxima [A]  time = 0.42, size = 12, normalized size = 0.75 \[ \frac {1}{3} \, x^{3} + \frac {1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*x^3 + 1/2*x^2 + x

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mupad [B]  time = 0.02, size = 13, normalized size = 0.81 \[ \frac {x\,\left (2\,x^2+3\,x+6\right )}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x + x^2 + 1,x)

[Out]

(x*(3*x + 2*x^2 + 6))/6

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sympy [A]  time = 0.05, size = 10, normalized size = 0.62 \[ \frac {x^{3}}{3} + \frac {x^{2}}{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2+x+1,x)

[Out]

x**3/3 + x**2/2 + x

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