3.28.41 \(\int (-4 x^3+4 e x^3) \, dx\)

Optimal. Leaf size=14 \[ -x^3 (x-e x)+\log (3) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {6, 12, 30} \begin {gather*} -\left ((1-e) x^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4*x^3 + 4*E*x^3,x]

[Out]

-((1 - E)*x^4)

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int (-4+4 e) x^3 \, dx\\ &=-\left ((4 (1-e)) \int x^3 \, dx\right )\\ &=-\left ((1-e) x^4\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} -x^4+e x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4*x^3 + 4*E*x^3,x]

[Out]

-x^4 + E*x^4

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fricas [A]  time = 0.48, size = 12, normalized size = 0.86 \begin {gather*} x^{4} e - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3*exp(1)-4*x^3,x, algorithm="fricas")

[Out]

x^4*e - x^4

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giac [A]  time = 0.16, size = 12, normalized size = 0.86 \begin {gather*} x^{4} e - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3*exp(1)-4*x^3,x, algorithm="giac")

[Out]

x^4*e - x^4

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maple [A]  time = 0.02, size = 9, normalized size = 0.64

method	result	size
gosper	\(x^{4} \left ({\mathrm e}-1\right )\)	\(9\)
norman	\(x^{4} \left ({\mathrm e}-1\right )\)	\(9\)
default	\(x^{4} {\mathrm e}-x^{4}\)	\(13\)
risch	\(x^{4} {\mathrm e}-x^{4}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^3*exp(1)-4*x^3,x,method=_RETURNVERBOSE)

[Out]

x^4*(exp(1)-1)

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maxima [A]  time = 0.46, size = 12, normalized size = 0.86 \begin {gather*} x^{4} e - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3*exp(1)-4*x^3,x, algorithm="maxima")

[Out]

x^4*e - x^4

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mupad [B]  time = 1.78, size = 8, normalized size = 0.57 \begin {gather*} x^4\,\left (\mathrm {e}-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^3*exp(1) - 4*x^3,x)

[Out]

x^4*(exp(1) - 1)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.50 \begin {gather*} x^{4} \left (-1 + e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x**3*exp(1)-4*x**3,x)

[Out]

x**4*(-1 + E)

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