3.76.83 \(\int \frac {1}{5} (-6 x+1024 e^4 x^3) \, dx\)

Optimal. Leaf size=17 \[ \frac {1}{5} x^2 \left (-3+256 e^4 x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.06, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \begin {gather*} \frac {256 e^4 x^4}{5}-\frac {3 x^2}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-6*x + 1024*E^4*x^3)/5,x]

[Out]

(-3*x^2)/5 + (256*E^4*x^4)/5

Rule 12

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-6 x+1024 e^4 x^3\right ) \, dx\\ &=-\frac {3 x^2}{5}+\frac {256 e^4 x^4}{5}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 20, normalized size = 1.18 \begin {gather*} \frac {2}{5} \left (-\frac {3 x^2}{2}+128 e^4 x^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*x + 1024*E^4*x^3)/5,x]

[Out]

(2*((-3*x^2)/2 + 128*E^4*x^4))/5

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fricas [A]  time = 0.85, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1024/5*x^3*exp(2)^2-6/5*x,x, algorithm="fricas")

[Out]

256/5*x^4*e^4 - 3/5*x^2

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giac [A]  time = 0.15, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1024/5*x^3*exp(2)^2-6/5*x,x, algorithm="giac")

[Out]

256/5*x^4*e^4 - 3/5*x^2

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maple [A]  time = 0.02, size = 14, normalized size = 0.82

method	result	size
risch	\(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\)	\(14\)
default	\(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\)	\(16\)
norman	\(\frac {256 x^{4} {\mathrm e}^{4}}{5}-\frac {3 x^{2}}{5}\)	\(16\)
gosper	\(\frac {\left (256 x^{2} {\mathrm e}^{4}-3\right ) x^{2}}{5}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1024/5*x^3*exp(2)^2-6/5*x,x,method=_RETURNVERBOSE)

[Out]

256/5*x^4*exp(4)-3/5*x^2

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maxima [A]  time = 0.35, size = 13, normalized size = 0.76 \begin {gather*} \frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1024/5*x^3*exp(2)^2-6/5*x,x, algorithm="maxima")

[Out]

256/5*x^4*e^4 - 3/5*x^2

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mupad [B]  time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} \frac {x^2\,\left (256\,x^2\,{\mathrm {e}}^4-3\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1024*x^3*exp(4))/5 - (6*x)/5,x)

[Out]

(x^2*(256*x^2*exp(4) - 3))/5

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sympy [A]  time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} \frac {256 x^{4} e^{4}}{5} - \frac {3 x^{2}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1024/5*x**3*exp(2)**2-6/5*x,x)

[Out]

256*x**4*exp(4)/5 - 3*x**2/5

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