3.1898 \(\int (3-5 x+2 x^2) \, dx\)

Optimal. Leaf size=18 \[ \frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x \]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

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Rubi [A]  time = 0.0025386, antiderivative size = 18, 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 = {} \[ \frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Int[3 - 5*x + 2*x^2,x]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

Rubi steps

\begin{align*} \int \left (3-5 x+2 x^2\right ) \, dx &=3 x-\frac{5 x^2}{2}+\frac{2 x^3}{3}\\ \end{align*}

Mathematica [A]  time = 0.0000442, size = 18, normalized size = 1. \[ \frac{2 x^3}{3}-\frac{5 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Integrate[3 - 5*x + 2*x^2,x]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

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Maple [A]  time = 0.001, size = 15, normalized size = 0.8 \begin{align*} 3\,x-{\frac{5\,{x}^{2}}{2}}+{\frac{2\,{x}^{3}}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x^2-5*x+3,x)

[Out]

3*x-5/2*x^2+2/3*x^3

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Maxima [A]  time = 0.949765, size = 19, normalized size = 1.06 \begin{align*} \frac{2}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^2-5*x+3,x, algorithm="maxima")

[Out]

2/3*x^3 - 5/2*x^2 + 3*x

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Fricas [A]  time = 1.86253, size = 34, normalized size = 1.89 \begin{align*} \frac{2}{3} x^{3} - \frac{5}{2} x^{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^2-5*x+3,x, algorithm="fricas")

[Out]

2/3*x^3 - 5/2*x^2 + 3*x

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Sympy [A]  time = 0.051925, size = 15, normalized size = 0.83 \begin{align*} \frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} + 3 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x**2-5*x+3,x)

[Out]

2*x**3/3 - 5*x**2/2 + 3*x

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Giac [A]  time = 1.0569, size = 19, normalized size = 1.06 \begin{align*} \frac{2}{3} \, x^{3} - \frac{5}{2} \, x^{2} + 3 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^2-5*x+3,x, algorithm="giac")

[Out]

2/3*x^3 - 5/2*x^2 + 3*x