3.78.33 \(\int 2 e^4 x^7 \, dx\)

Optimal. Leaf size=10 \[ \frac {e^4 x^8}{4} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {e^4 x^8}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*E^4*x^7,x]

[Out]

(E^4*x^8)/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 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (2 e^4\right ) \int x^7 \, dx\\ &=\frac {e^4 x^8}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {e^4 x^8}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*E^4*x^7,x]

[Out]

(E^4*x^8)/4

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fricas [A]  time = 0.60, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{4} \, x^{8} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="fricas")

[Out]

1/4*x^8*e^4

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giac [A]  time = 0.14, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{4} \, x^{8} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="giac")

[Out]

1/4*x^8*e^4

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maple [A]  time = 0.02, size = 8, normalized size = 0.80

method	result	size
risch	\(\frac {x^{8} {\mathrm e}^{4}}{4}\)	\(8\)
gosper	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)
default	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)
norman	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x^7*exp(3)^4/exp(2)^4,x,method=_RETURNVERBOSE)

[Out]

1/4*x^8*exp(4)

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maxima [A]  time = 0.37, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{4} \, x^{8} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="maxima")

[Out]

1/4*x^8*e^4

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mupad [B]  time = 0.04, size = 7, normalized size = 0.70 \begin {gather*} \frac {x^8\,{\mathrm {e}}^4}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x^7*exp(4),x)

[Out]

(x^8*exp(4))/4

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sympy [A]  time = 0.05, size = 7, normalized size = 0.70 \begin {gather*} \frac {x^{8} e^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x**7*exp(3)**4/exp(2)**4,x)

[Out]

x**8*exp(4)/4

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