\(\int (-3+6 x^2+4 x^3) \, dx\) [2690]

Optimal result

Integrand size = 12, antiderivative size = 18 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=-3 x-x^2+\left (x+x^2\right )^2+\log (3) \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^4+2 x^3-3 x \]

[In]

Int[-3 + 6*x^2 + 4*x^3,x]

[Out]

-3*x + 2*x^3 + x^4

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=-3 x+2 x^3+x^4 \]

[In]

Integrate[-3 + 6*x^2 + 4*x^3,x]

[Out]

-3*x + 2*x^3 + x^4

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72

method	result	size
gosper	\(x^{4}+2 x^{3}-3 x\)	\(13\)
default	\(x^{4}+2 x^{3}-3 x\)	\(13\)
norman	\(x^{4}+2 x^{3}-3 x\)	\(13\)
risch	\(x^{4}+2 x^{3}-3 x\)	\(13\)
parallelrisch	\(x^{4}+2 x^{3}-3 x\)	\(13\)
parts	\(x^{4}+2 x^{3}-3 x\)	\(13\)

[In]

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

[Out]

x^4+2*x^3-3*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.56 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 x^{3} - 3 x \]

[In]

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

[Out]

x**4 + 2*x**3 - 3*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x\,\left (x^3+2\,x^2-3\right ) \]

[In]

int(6*x^2 + 4*x^3 - 3,x)

[Out]

x*(2*x^2 + x^3 - 3)