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

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

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 18, 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 {2 x^3}{3}-\frac {5 x^2}{2}+3 x \end {gather*}

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 = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {2 x^3}{3}-\frac {5 x^2}{2}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 - 5*x + 2*x^2,x]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (3-5 x+2 x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[3 - 5*x + 2*x^2,x]

[Out]

IntegrateAlgebraic[3 - 5*x + 2*x^2, x]

________________________________________________________________________________________

fricas [A]  time = 0.49, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{3} x^{3} - \frac {5}{2} x^{2} + 3 x \end {gather*}

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

________________________________________________________________________________________

giac [A]  time = 0.85, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 3 \, x \end {gather*}

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

________________________________________________________________________________________

maple [A]  time = 0.00, size = 15, normalized size = 0.83 \begin {gather*} \frac {2}{3} x^{3}-\frac {5}{2} x^{2}+3 x \end {gather*}

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

________________________________________________________________________________________

maxima [A]  time = 0.97, size = 14, normalized size = 0.78 \begin {gather*} \frac {2}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 3 \, x \end {gather*}

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

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 13, normalized size = 0.72 \begin {gather*} \frac {x\,\left (4\,x^2-15\,x+18\right )}{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x^2 - 5*x + 3,x)

[Out]

(x*(4*x^2 - 15*x + 18))/6

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} \frac {2 x^{3}}{3} - \frac {5 x^{2}}{2} + 3 x \end {gather*}

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

________________________________________________________________________________________