3.42.15 \(\int -\frac {48828125}{7558272 e^{16} x^{11}} \, dx\)

Optimal. Leaf size=10 \[ \frac {9765625}{15116544 e^{16} x^{10}} \]

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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 = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} \frac {9765625}{15116544 e^{16} x^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-48828125/(7558272*E^16*x^11),x]

[Out]

9765625/(15116544*E^16*x^10)

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 {48828125 \int \frac {1}{x^{11}} \, dx}{7558272 e^{16}}\\ &=\frac {9765625}{15116544 e^{16} x^{10}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {9765625}{15116544 e^{16} x^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-48828125/(7558272*E^16*x^11),x]

[Out]

9765625/(15116544*E^16*x^10)

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fricas [A]  time = 0.70, size = 7, normalized size = 0.70 \begin {gather*} \frac {9765625 \, e^{\left (-16\right )}}{15116544 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-48828125/7558272/x^11/exp(16),x, algorithm="fricas")

[Out]

9765625/15116544*e^(-16)/x^10

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giac [A]  time = 0.13, size = 7, normalized size = 0.70 \begin {gather*} \frac {9765625 \, e^{\left (-16\right )}}{15116544 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-48828125/7558272/x^11/exp(16),x, algorithm="giac")

[Out]

9765625/15116544*e^(-16)/x^10

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maple [A]  time = 0.03, size = 8, normalized size = 0.80

method	result	size
risch	\(\frac {9765625 \,{\mathrm e}^{-16}}{15116544 x^{10}}\)	\(8\)
gosper	\(\frac {9765625 \,{\mathrm e}^{-16}}{15116544 x^{10}}\)	\(10\)
default	\(\frac {9765625 \,{\mathrm e}^{-16}}{15116544 x^{10}}\)	\(10\)
norman	\(\frac {9765625 \,{\mathrm e}^{-16}}{15116544 x^{10}}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-48828125/7558272/x^11/exp(16),x,method=_RETURNVERBOSE)

[Out]

9765625/15116544/x^10*exp(-16)

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maxima [A]  time = 0.35, size = 7, normalized size = 0.70 \begin {gather*} \frac {9765625 \, e^{\left (-16\right )}}{15116544 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-48828125/7558272/x^11/exp(16),x, algorithm="maxima")

[Out]

9765625/15116544*e^(-16)/x^10

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mupad [B]  time = 0.05, size = 7, normalized size = 0.70 \begin {gather*} \frac {9765625\,{\mathrm {e}}^{-16}}{15116544\,x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(48828125*exp(-16))/(7558272*x^11),x)

[Out]

(9765625*exp(-16))/(15116544*x^10)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.80 \begin {gather*} \frac {9765625}{15116544 x^{10} e^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-48828125/7558272/x**11/exp(16),x)

[Out]

9765625*exp(-16)/(15116544*x**10)

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