3.19.98 \(\int (3-5 x+2 x^2) \, dx\) [1898]

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

[Out]

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

________________________________________________________________________________________

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*} 3 x-\frac {5 x^2}{2}+\frac {2 x^3}{3} \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

________________________________________________________________________________________

Maple [A]
time = 0.01, size = 15, normalized size = 0.83

method	result	size
gosper	\(\frac {x \left (4 x^{2}-15 x +18\right )}{6}\)	\(14\)
default	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)
norman	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)
risch	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.27, 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

________________________________________________________________________________________

Fricas [A]
time = 0.67, 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

________________________________________________________________________________________

Sympy [A]
time = 0.01, 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

________________________________________________________________________________________

Giac [A]
time = 0.86, 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

________________________________________________________________________________________

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

________________________________________________________________________________________