3.22.78 \(\int \frac {12058624 x^{22}}{e^6} \, dx\)

Optimal. Leaf size=8 \[ \frac {524288 x^{23}}{e^6} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, 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 {524288 x^{23}}{e^6} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(12058624*x^22)/E^6,x]

[Out]

(524288*x^23)/E^6

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} &=\frac {12058624 \int x^{22} \, dx}{e^6}\\ &=\frac {524288 x^{23}}{e^6}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {524288 x^{23}}{e^6} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(12058624*x^22)/E^6,x]

[Out]

(524288*x^23)/E^6

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fricas [A]  time = 0.48, size = 7, normalized size = 0.88 \begin {gather*} 524288 \, x^{23} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="fricas")

[Out]

524288*x^23*e^(-6)

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giac [A]  time = 0.18, size = 7, normalized size = 0.88 \begin {gather*} 524288 \, x^{23} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="giac")

[Out]

524288*x^23*e^(-6)

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maple [A]  time = 0.04, size = 8, normalized size = 1.00

method	result	size
risch	\(524288 x^{23} {\mathrm e}^{-6}\)	\(8\)
gosper	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)
default	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)
norman	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12058624*x^22/exp(3)^2,x,method=_RETURNVERBOSE)

[Out]

524288*x^23*exp(-6)

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maxima [A]  time = 0.54, size = 7, normalized size = 0.88 \begin {gather*} 524288 \, x^{23} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="maxima")

[Out]

524288*x^23*e^(-6)

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mupad [B]  time = 0.02, size = 7, normalized size = 0.88 \begin {gather*} 524288\,x^{23}\,{\mathrm {e}}^{-6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12058624*x^22*exp(-6),x)

[Out]

524288*x^23*exp(-6)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.88 \begin {gather*} \frac {524288 x^{23}}{e^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(12058624*x**22/exp(3)**2,x)

[Out]

524288*x**23*exp(-6)

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