\(\int 1125 e^{-2+225 x^5} x^4 \, dx\) [2016]

Optimal result

Integrand size = 14, antiderivative size = 9 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{-2+225 x^5} \]

[Out]

exp(225*x^5-2)

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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2240} \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{225 x^5-2} \]

[In]

Int[1125*E^(-2 + 225*x^5)*x^4,x]

[Out]

E^(-2 + 225*x^5)

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}& = 1125 \int e^{-2+225 x^5} x^4 \, dx \\ & = e^{-2+225 x^5} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{-2+225 x^5} \]

[In]

Integrate[1125*E^(-2 + 225*x^5)*x^4,x]

[Out]

E^(-2 + 225*x^5)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00

method	result	size
gosper	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
derivativedivides	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
default	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
norman	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
risch	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
parallelrisch	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
meijerg	\(-{\mathrm e}^{-2} \left (1-{\mathrm e}^{225 x^{5}}\right )\)	\(15\)

[In]

int(1125*x^4*exp(225*x^5-2),x,method=_RETURNVERBOSE)

[Out]

exp(225*x^5-2)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]

[In]

integrate(1125*x^4*exp(225*x^5-2),x, algorithm="fricas")

[Out]

e^(225*x^5 - 2)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{225 x^{5} - 2} \]

[In]

integrate(1125*x**4*exp(225*x**5-2),x)

[Out]

exp(225*x**5 - 2)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]

[In]

integrate(1125*x^4*exp(225*x^5-2),x, algorithm="maxima")

[Out]

e^(225*x^5 - 2)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx=e^{\left (225 \, x^{5} - 2\right )} \]

[In]

integrate(1125*x^4*exp(225*x^5-2),x, algorithm="giac")

[Out]

e^(225*x^5 - 2)

Mupad [B] (verification not implemented)

Time = 8.49 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 1125 e^{-2+225 x^5} x^4 \, dx={\mathrm {e}}^{-2}\,{\mathrm {e}}^{225\,x^5} \]

[In]

int(1125*x^4*exp(225*x^5 - 2),x)

[Out]

exp(-2)*exp(225*x^5)