\(\int (36 x+9 x^2) \, dx\) [1607]

Optimal result

Integrand size = 9, antiderivative size = 8 \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^2 (6+x) \]

[Out]

3*x^2*(6+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^3+18 x^2 \]

[In]

Int[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

Rubi steps \begin{align*} \text {integral}& = 18 x^2+3 x^3 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=18 x^2+3 x^3 \]

[In]

Integrate[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12

method	result	size
gosper	\(3 x^{2} \left (6+x \right )\)	\(9\)
default	\(3 x^{3}+18 x^{2}\)	\(12\)
norman	\(3 x^{3}+18 x^{2}\)	\(12\)
risch	\(3 x^{3}+18 x^{2}\)	\(12\)
parallelrisch	\(3 x^{3}+18 x^{2}\)	\(12\)
parts	\(3 x^{3}+18 x^{2}\)	\(12\)

[In]

int(9*x^2+36*x,x,method=_RETURNVERBOSE)

[Out]

3*x^2*(6+x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]

[In]

integrate(9*x^2+36*x,x, algorithm="fricas")

[Out]

3*x^3 + 18*x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \left (36 x+9 x^2\right ) \, dx=3 x^{3} + 18 x^{2} \]

[In]

integrate(9*x**2+36*x,x)

[Out]

3*x**3 + 18*x**2

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]

[In]

integrate(9*x^2+36*x,x, algorithm="maxima")

[Out]

3*x^3 + 18*x^2

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.38 \[ \int \left (36 x+9 x^2\right ) \, dx=3 \, x^{3} + 18 \, x^{2} \]

[In]

integrate(9*x^2+36*x,x, algorithm="giac")

[Out]

3*x^3 + 18*x^2

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \left (36 x+9 x^2\right ) \, dx=3\,x^2\,\left (x+6\right ) \]

[In]

int(36*x + 9*x^2,x)

[Out]

3*x^2*(x + 6)