3.29.77 \(\int \frac {5}{4} e^{\frac {x^5}{4}} x^4 \, dx\)

Optimal. Leaf size=9 \[ e^{\frac {x^5}{4}} \]

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Rubi [A]  time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2209} \begin {gather*} e^{\frac {x^5}{4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(5*E^(x^5/4)*x^4)/4,x]

[Out]

E^(x^5/4)

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} &=\frac {5}{4} \int e^{\frac {x^5}{4}} x^4 \, dx\\ &=e^{\frac {x^5}{4}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} e^{\frac {x^5}{4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5*E^(x^5/4)*x^4)/4,x]

[Out]

E^(x^5/4)

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fricas [A]  time = 0.87, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (\frac {1}{4} \, x^{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/4*x^4*exp(1/4*x^5),x, algorithm="fricas")

[Out]

e^(1/4*x^5)

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giac [A]  time = 0.18, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (\frac {1}{4} \, x^{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/4*x^4*exp(1/4*x^5),x, algorithm="giac")

[Out]

e^(1/4*x^5)

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maple [A]  time = 0.03, size = 7, normalized size = 0.78

method	result	size
gosper	\({\mathrm e}^{\frac {x^{5}}{4}}\)	\(7\)
derivativedivides	\({\mathrm e}^{\frac {x^{5}}{4}}\)	\(7\)
default	\({\mathrm e}^{\frac {x^{5}}{4}}\)	\(7\)
norman	\({\mathrm e}^{\frac {x^{5}}{4}}\)	\(7\)
risch	\({\mathrm e}^{\frac {x^{5}}{4}}\)	\(7\)
meijerg	\(-1+{\mathrm e}^{\frac {x^{5}}{4}}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5/4*x^4*exp(1/4*x^5),x,method=_RETURNVERBOSE)

[Out]

exp(1/4*x^5)

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maxima [A]  time = 0.35, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (\frac {1}{4} \, x^{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/4*x^4*exp(1/4*x^5),x, algorithm="maxima")

[Out]

e^(1/4*x^5)

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mupad [B]  time = 1.67, size = 6, normalized size = 0.67 \begin {gather*} {\mathrm {e}}^{\frac {x^5}{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*x^4*exp(x^5/4))/4,x)

[Out]

exp(x^5/4)

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sympy [A]  time = 0.08, size = 5, normalized size = 0.56 \begin {gather*} e^{\frac {x^{5}}{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/4*x**4*exp(1/4*x**5),x)

[Out]

exp(x**5/4)

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