\(\int \frac {1}{5} (-6 x+1024 e^4 x^3) \, dx\) [7583]

Optimal result

Integrand size = 16, antiderivative size = 17 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {1}{5} x^2 \left (-3+256 e^4 x^2\right ) \]

[Out]

1/5*(256*x^2*exp(2)^2-3)*x^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {256 e^4 x^4}{5}-\frac {3 x^2}{5} \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.18 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {2}{5} \left (-\frac {3 x^2}{2}+128 e^4 x^4\right ) \]

[In]

Integrate[(-6*x + 1024*E^4*x^3)/5,x]

[Out]

(2*((-3*x^2)/2 + 128*E^4*x^4))/5

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82

method	result	size
risch	\(-\frac {3 x^{2}}{5}+\frac {256 x^{4} {\mathrm e}^{4}}{5}\)	\(14\)
norman	\(-\frac {3 x^{2}}{5}+\frac {256 x^{4} {\mathrm e}^{4}}{5}\)	\(16\)
parallelrisch	\(-\frac {3 x^{2}}{5}+\frac {256 x^{4} {\mathrm e}^{4}}{5}\)	\(16\)
parts	\(-\frac {3 x^{2}}{5}+\frac {256 x^{4} {\mathrm e}^{4}}{5}\)	\(16\)
gosper	\(\frac {\left (256 x^{2} {\mathrm e}^{4}-3\right ) x^{2}}{5}\)	\(17\)
default	\(\frac {\left (512 x^{2} {\mathrm e}^{4}-3\right )^{2} {\mathrm e}^{-4}}{5120}\)	\(20\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \]

[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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {256 x^{4} e^{4}}{5} - \frac {3 x^{2}}{5} \]

[In]

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

[Out]

256*x**4*exp(4)/5 - 3*x**2/5

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \]

[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

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {256}{5} \, x^{4} e^{4} - \frac {3}{5} \, x^{2} \]

[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

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {1}{5} \left (-6 x+1024 e^4 x^3\right ) \, dx=\frac {x^2\,\left (256\,x^2\,{\mathrm {e}}^4-3\right )}{5} \]

[In]

int((1024*x^3*exp(4))/5 - (6*x)/5,x)

[Out]

(x^2*(256*x^2*exp(4) - 3))/5