3.82.35 \(\int \frac {20 x^9 \log ^8(5)}{9 e^{24}} \, dx\)

Optimal. Leaf size=14 \[ \frac {2 x^{10} \log ^8(5)}{9 e^{24}} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, 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, 30} \begin {gather*} \frac {2 x^{10} \log ^8(5)}{9 e^{24}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(20*x^9*Log[5]^8)/(9*E^24),x]

[Out]

(2*x^10*Log[5]^8)/(9*E^24)

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 {\left (20 \log ^8(5)\right ) \int x^9 \, dx}{9 e^{24}}\\ &=\frac {2 x^{10} \log ^8(5)}{9 e^{24}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 x^{10} \log ^8(5)}{9 e^{24}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(20*x^9*Log[5]^8)/(9*E^24),x]

[Out]

(2*x^10*Log[5]^8)/(9*E^24)

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fricas [A]  time = 0.74, size = 11, normalized size = 0.79 \begin {gather*} \frac {2}{9} \, x^{10} e^{\left (-24\right )} \log \relax (5)^{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20/9*x^9*log(5)^8/exp(3)^8,x, algorithm="fricas")

[Out]

2/9*x^10*e^(-24)*log(5)^8

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giac [A]  time = 0.14, size = 11, normalized size = 0.79 \begin {gather*} \frac {2}{9} \, x^{10} e^{\left (-24\right )} \log \relax (5)^{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20/9*x^9*log(5)^8/exp(3)^8,x, algorithm="giac")

[Out]

2/9*x^10*e^(-24)*log(5)^8

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maple [A]  time = 0.03, size = 12, normalized size = 0.86

method	result	size
risch	\(\frac {2 x^{10} \ln \relax (5)^{8} {\mathrm e}^{-24}}{9}\)	\(12\)
gosper	\(\frac {2 x^{10} \ln \relax (5)^{8} {\mathrm e}^{-24}}{9}\)	\(14\)
default	\(\frac {2 x^{10} \ln \relax (5)^{8} {\mathrm e}^{-24}}{9}\)	\(14\)
norman	\(\frac {2 x^{10} \ln \relax (5)^{8} {\mathrm e}^{-24}}{9}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20/9*x^9*ln(5)^8/exp(3)^8,x,method=_RETURNVERBOSE)

[Out]

2/9*x^10*ln(5)^8*exp(-24)

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maxima [A]  time = 0.37, size = 11, normalized size = 0.79 \begin {gather*} \frac {2}{9} \, x^{10} e^{\left (-24\right )} \log \relax (5)^{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20/9*x^9*log(5)^8/exp(3)^8,x, algorithm="maxima")

[Out]

2/9*x^10*e^(-24)*log(5)^8

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mupad [B]  time = 5.48, size = 11, normalized size = 0.79 \begin {gather*} \frac {2\,x^{10}\,{\mathrm {e}}^{-24}\,{\ln \relax (5)}^8}{9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((20*x^9*exp(-24)*log(5)^8)/9,x)

[Out]

(2*x^10*exp(-24)*log(5)^8)/9

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sympy [A]  time = 0.05, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 x^{10} \log {\relax (5 )}^{8}}{9 e^{24}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20/9*x**9*ln(5)**8/exp(3)**8,x)

[Out]

2*x**10*exp(-24)*log(5)**8/9

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