\(\int (-3-10 x-6 x^2-4 x^3) \, dx\) [9630]

Optimal result

Integrand size = 15, antiderivative size = 17 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-e^{17}+x-\left (2+x+x^2\right )^2 \]

[Out]

x-(x^2+x+2)^2-exp(17)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-x^4-2 x^3-5 x^2-3 x \]

[In]

Int[-3 - 10*x - 6*x^2 - 4*x^3,x]

[Out]

-3*x - 5*x^2 - 2*x^3 - x^4

Rubi steps \begin{align*} \text {integral}& = -3 x-5 x^2-2 x^3-x^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-3 x-5 x^2-2 x^3-x^4 \]

[In]

Integrate[-3 - 10*x - 6*x^2 - 4*x^3,x]

[Out]

-3*x - 5*x^2 - 2*x^3 - x^4

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00

method	result	size
gosper	\(-x \left (x^{3}+2 x^{2}+5 x +3\right )\)	\(17\)
default	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
norman	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
risch	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
parallelrisch	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)
parts	\(-x^{4}-2 x^{3}-5 x^{2}-3 x\)	\(20\)

[In]

int(-4*x^3-6*x^2-10*x-3,x,method=_RETURNVERBOSE)

[Out]

-x*(x^3+2*x^2+5*x+3)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \]

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="fricas")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=- x^{4} - 2 x^{3} - 5 x^{2} - 3 x \]

[In]

integrate(-4*x**3-6*x**2-10*x-3,x)

[Out]

-x**4 - 2*x**3 - 5*x**2 - 3*x

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \]

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="maxima")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-x^{4} - 2 \, x^{3} - 5 \, x^{2} - 3 \, x \]

[In]

integrate(-4*x^3-6*x^2-10*x-3,x, algorithm="giac")

[Out]

-x^4 - 2*x^3 - 5*x^2 - 3*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \left (-3-10 x-6 x^2-4 x^3\right ) \, dx=-x^4-2\,x^3-5\,x^2-3\,x \]

[In]

int(- 10*x - 6*x^2 - 4*x^3 - 3,x)

[Out]

- 3*x - 5*x^2 - 2*x^3 - x^4