3.26.96 \(\int -\frac {1}{4 e^{20} x^2} \, dx\)

Optimal. Leaf size=10 \[ \frac {1}{4 e^{20} x} \]

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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 {1}{4 e^{20} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/4*1/(E^20*x^2),x]

[Out]

1/(4*E^20*x)

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 {\int \frac {1}{x^2} \, dx}{4 e^{20}}\\ &=\frac {1}{4 e^{20} x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {1}{4 e^{20} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/4*1/(E^20*x^2),x]

[Out]

1/(4*E^20*x)

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fricas [A]  time = 0.58, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/4*exp(x)/x/exp(log(x)+20+x),x, algorithm="fricas")

[Out]

1/4*e^(-20)/x

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giac [A]  time = 0.18, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/4*exp(x)/x/exp(log(x)+20+x),x, algorithm="giac")

[Out]

1/4*e^(-20)/x

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maple [A]  time = 0.15, size = 8, normalized size = 0.80

method	result	size
default	\(\frac {{\mathrm e}^{-20}}{4 x}\)	\(8\)
risch	\(\frac {{\mathrm e}^{-20}}{4 x}\)	\(8\)
norman	\(\frac {{\mathrm e}^{-20}}{4 x}\)	\(10\)
gosper	\(\frac {{\mathrm e}^{x} {\mathrm e}^{-20-x}}{4 x}\)	\(13\)
meijerg	\(-\frac {\left (-1\right )^{{\mathrm e}^{-20}} x^{{\mathrm e}^{-20}-1} {\mathrm e}^{-20-x} \left (-\frac {{\mathrm e}^{20} x^{-{\mathrm e}^{-20}} \left (-1\right )^{-{\mathrm e}^{-20}} \left (x \,{\mathrm e}^{20}+{\mathrm e}^{20}-1\right ) \Gamma \left (1+{\mathrm e}^{-20}\right ) \Gamma \left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right ) L_{{\mathrm e}^{-20}}^{\left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}\right )}\relax (x )}{\left ({\mathrm e}^{20}-1\right ) \Gamma \left ({\mathrm e}^{-20}+\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}+\frac {{\mathrm e}^{40} x^{1-{\mathrm e}^{-20}} \left (-1\right )^{-{\mathrm e}^{-20}} L_{{\mathrm e}^{-20}}^{\left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}\relax (x ) \Gamma \left (1+{\mathrm e}^{-20}\right ) \Gamma \left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}{\left ({\mathrm e}^{20}-1\right ) \Gamma \left ({\mathrm e}^{-20}+\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}\right )}{4}\)	\(155\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/4*exp(x)/x/exp(ln(x)+20+x),x,method=_RETURNVERBOSE)

[Out]

1/4*exp(-20)/x

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maxima [A]  time = 0.44, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/4*exp(x)/x/exp(log(x)+20+x),x, algorithm="maxima")

[Out]

1/4*e^(-20)/x

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mupad [B]  time = 1.39, size = 7, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^{-20}}{4\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*exp(- x - log(x) - 20))/(4*x),x)

[Out]

exp(-20)/(4*x)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{4 x e^{20}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/4*exp(x)/x/exp(ln(x)+20+x),x)

[Out]

exp(-20)/(4*x)

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