\(\int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx\) [2288]

Optimal result

Integrand size = 16, antiderivative size = 9 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\frac {136 x^4}{3}} \]

[Out]

exp(136/3*x^4)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2240} \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\frac {136 x^4}{3}} \]

[In]

Int[(544*E^((136*x^4)/3)*x^3)/3,x]

[Out]

E^((136*x^4)/3)

Rule 12

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

Rule 2240

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[(e + f*x)^n*(
F^(a + b*(c + d*x)^n)/(b*f*n*(c + d*x)^n*Log[F])), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps \begin{align*} \text {integral}& = \frac {544}{3} \int e^{\frac {136 x^4}{3}} x^3 \, dx \\ & = e^{\frac {136 x^4}{3}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\frac {136 x^4}{3}} \]

[In]

Integrate[(544*E^((136*x^4)/3)*x^3)/3,x]

[Out]

E^((136*x^4)/3)

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

method	result	size
gosper	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
derivativedivides	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
default	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
norman	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
risch	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
parallelrisch	\({\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(7\)
meijerg	\(-1+{\mathrm e}^{\frac {136 x^{4}}{3}}\)	\(9\)

[In]

int(544/3*x^3*exp(136/3*x^4),x,method=_RETURNVERBOSE)

[Out]

exp(136/3*x^4)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\left (\frac {136}{3} \, x^{4}\right )} \]

[In]

integrate(544/3*x^3*exp(136/3*x^4),x, algorithm="fricas")

[Out]

e^(136/3*x^4)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\frac {136 x^{4}}{3}} \]

[In]

integrate(544/3*x**3*exp(136/3*x**4),x)

[Out]

exp(136*x**4/3)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\left (\frac {136}{3} \, x^{4}\right )} \]

[In]

integrate(544/3*x^3*exp(136/3*x^4),x, algorithm="maxima")

[Out]

e^(136/3*x^4)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx=e^{\left (\frac {136}{3} \, x^{4}\right )} \]

[In]

integrate(544/3*x^3*exp(136/3*x^4),x, algorithm="giac")

[Out]

e^(136/3*x^4)

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {544}{3} e^{\frac {136 x^4}{3}} x^3 \, dx={\mathrm {e}}^{\frac {136\,x^4}{3}} \]

[In]

int((544*x^3*exp((136*x^4)/3))/3,x)

[Out]

exp((136*x^4)/3)