\(\int (2 x+5 x^2) \, dx\) [1896]

Optimal result

Integrand size = 9, antiderivative size = 11 \[ \int \left (2 x+5 x^2\right ) \, dx=x^2+\frac {5 x^3}{3} \]

[Out]

x^2+5/3*x^3

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, 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 = {} \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {5 x^3}{3}+x^2 \]

[In]

Int[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (2 x+5 x^2\right ) \, dx=x^2+\frac {5 x^3}{3} \]

[In]

Integrate[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91

method	result	size
default	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
norman	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
risch	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
parallelrisch	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
parts	\(x^{2}+\frac {5}{3} x^{3}\)	\(10\)
gosper	\(\frac {x^{2} \left (3+5 x \right )}{3}\)	\(11\)

[In]

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

[Out]

x^2+5/3*x^3

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {5}{3} \, x^{3} + x^{2} \]

[In]

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

[Out]

5/3*x^3 + x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {5 x^{3}}{3} + x^{2} \]

[In]

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

[Out]

5*x**3/3 + x**2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {5}{3} \, x^{3} + x^{2} \]

[In]

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

[Out]

5/3*x^3 + x^2

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {5}{3} \, x^{3} + x^{2} \]

[In]

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

[Out]

5/3*x^3 + x^2

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (2 x+5 x^2\right ) \, dx=\frac {x^2\,\left (5\,x+3\right )}{3} \]

[In]

int(2*x + 5*x^2,x)

[Out]

(x^2*(5*x + 3))/3