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

Optimal. Leaf size=9 \[ e^{-2+225 x^5} \]

________________________________________________________________________________________

Rubi [A]  time = 0.03, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2209} \begin {gather*} e^{225 x^5-2} \end {gather*}

Antiderivative was successfully verified.

[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 2209

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 {gather*} \begin {aligned} \text {integral} &=1125 \int e^{-2+225 x^5} x^4 \, dx\\ &=e^{-2+225 x^5}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} e^{-2+225 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^(-2 + 225*x^5)

________________________________________________________________________________________

fricas [A]  time = 0.61, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (225 \, x^{5} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(225*x^5 - 2)

________________________________________________________________________________________

giac [A]  time = 0.28, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (225 \, x^{5} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(225*x^5 - 2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 9, normalized size = 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	\({\mathrm e}^{225 x^{5}-2}\)	\(9\)
meijerg	\(-{\mathrm e}^{-2} \left (1-{\mathrm e}^{225 x^{5}}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(225*x^5-2)

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (225 \, x^{5} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(225*x^5 - 2)

________________________________________________________________________________________

mupad [B]  time = 1.11, size = 9, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{-2}\,{\mathrm {e}}^{225\,x^5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1125*x^4*exp(225*x^5 - 2),x)

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 7, normalized size = 0.78 \begin {gather*} e^{225 x^{5} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(225*x**5 - 2)

________________________________________________________________________________________