3.302 \(\int (-2 x+x^2+x^3) \, dx\)

Optimal. Leaf size=20 \[ \frac {x^4}{4}+\frac {x^3}{3}-x^2 \]

[Out]

-x^2+1/3*x^3+1/4*x^4

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Rubi [A]  time = 0.00, antiderivative size = 20, 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 = {} \[ \frac {x^4}{4}+\frac {x^3}{3}-x^2 \]

Antiderivative was successfully verified.

[In]

Int[-2*x + x^2 + x^3,x]

[Out]

-x^2 + x^3/3 + x^4/4

Rubi steps

\begin {align*} \int \left (-2 x+x^2+x^3\right ) \, dx &=-x^2+\frac {x^3}{3}+\frac {x^4}{4}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 20, normalized size = 1.00 \[ \frac {x^4}{4}+\frac {x^3}{3}-x^2 \]

Antiderivative was successfully verified.

[In]

Integrate[-2*x + x^2 + x^3,x]

[Out]

-x^2 + x^3/3 + x^4/4

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fricas [A]  time = 0.35, size = 16, normalized size = 0.80 \[ \frac {1}{4} x^{4} + \frac {1}{3} x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3+x^2-2*x,x, algorithm="fricas")

[Out]

1/4*x^4 + 1/3*x^3 - x^2

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giac [A]  time = 0.97, size = 16, normalized size = 0.80 \[ \frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3+x^2-2*x,x, algorithm="giac")

[Out]

1/4*x^4 + 1/3*x^3 - x^2

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maple [A]  time = 0.00, size = 17, normalized size = 0.85 \[ \frac {1}{4} x^{4}+\frac {1}{3} x^{3}-x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3+x^2-2*x,x)

[Out]

-x^2+1/3*x^3+1/4*x^4

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maxima [A]  time = 0.60, size = 16, normalized size = 0.80 \[ \frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3+x^2-2*x,x, algorithm="maxima")

[Out]

1/4*x^4 + 1/3*x^3 - x^2

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mupad [B]  time = 0.03, size = 15, normalized size = 0.75 \[ \frac {x^2\,\left (3\,x^2+4\,x-12\right )}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2 - 2*x + x^3,x)

[Out]

(x^2*(4*x + 3*x^2 - 12))/12

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sympy [A]  time = 0.06, size = 12, normalized size = 0.60 \[ \frac {x^{4}}{4} + \frac {x^{3}}{3} - x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**3+x**2-2*x,x)

[Out]

x**4/4 + x**3/3 - x**2

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