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

Optimal result

Integrand size = 10, antiderivative size = 18 \[ \int \left (3-5 x+2 x^2\right ) \, dx=3 x-\frac {5 x^2}{2}+\frac {2 x^3}{3} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {2 x^3}{3}-\frac {5 x^2}{2}+3 x \]

[In]

Int[3 - 5*x + 2*x^2,x]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

Rubi steps \begin{align*} \text {integral}& = 3 x-\frac {5 x^2}{2}+\frac {2 x^3}{3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \left (3-5 x+2 x^2\right ) \, dx=3 x-\frac {5 x^2}{2}+\frac {2 x^3}{3} \]

[In]

Integrate[3 - 5*x + 2*x^2,x]

[Out]

3*x - (5*x^2)/2 + (2*x^3)/3

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78

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	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)
parallelrisch	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)
parts	\(3 x -\frac {5}{2} x^{2}+\frac {2}{3} x^{3}\)	\(15\)

[In]

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

[Out]

1/6*x*(4*x^2-15*x+18)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {2}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 3 \, x \]

[In]

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

[Out]

2/3*x^3 - 5/2*x^2 + 3*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {2 x^{3}}{3} - \frac {5 x^{2}}{2} + 3 x \]

[In]

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

[Out]

2*x**3/3 - 5*x**2/2 + 3*x

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {2}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 3 \, x \]

[In]

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

[Out]

2/3*x^3 - 5/2*x^2 + 3*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {2}{3} \, x^{3} - \frac {5}{2} \, x^{2} + 3 \, x \]

[In]

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

[Out]

2/3*x^3 - 5/2*x^2 + 3*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \left (3-5 x+2 x^2\right ) \, dx=\frac {x\,\left (4\,x^2-15\,x+18\right )}{6} \]

[In]

int(2*x^2 - 5*x + 3,x)

[Out]

(x*(4*x^2 - 15*x + 18))/6