3.27.90 \(\int (-3+6 x^2+4 x^3) \, dx\)

Optimal. Leaf size=18 \[ -3 x-x^2+\left (x+x^2\right )^2+\log (3) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^4+2 x^3-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 + 6*x^2 + 4*x^3,x]

[Out]

-3*x + 2*x^3 + x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-3 x+2 x^3+x^4\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 12, normalized size = 0.67 \begin {gather*} -3 x+2 x^3+x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 + 6*x^2 + 4*x^3,x]

[Out]

-3*x + 2*x^3 + x^4

________________________________________________________________________________________

fricas [A]  time = 0.46, size = 12, normalized size = 0.67 \begin {gather*} x^{4} + 2 \, x^{3} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

________________________________________________________________________________________

giac [A]  time = 0.21, size = 12, normalized size = 0.67 \begin {gather*} x^{4} + 2 \, x^{3} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

________________________________________________________________________________________

maple [A]  time = 0.01, size = 13, normalized size = 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	\(x^{4}+2 x^{3}-3 x\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.57, size = 12, normalized size = 0.67 \begin {gather*} x^{4} + 2 \, x^{3} - 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^4 + 2*x^3 - 3*x

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 12, normalized size = 0.67 \begin {gather*} x\,\left (x^3+2\,x^2-3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x^2 + 4*x^3 - 3,x)

[Out]

x*(2*x^2 + x^3 - 3)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 10, normalized size = 0.56 \begin {gather*} x^{4} + 2 x^{3} - 3 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**4 + 2*x**3 - 3*x

________________________________________________________________________________________