3.88.59 \(\int \frac {e^{-5+x} (-15+x)}{3 x^{16}} \, dx\)

Optimal. Leaf size=14 \[ 1+\frac {e^{-5+x}}{3 x^{15}} \]

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Rubi [A]  time = 0.03, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2197} \begin {gather*} \frac {e^{x-5}}{3 x^{15}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(-5 + x)*(-15 + x))/(3*x^16),x]

[Out]

E^(-5 + x)/(3*x^15)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2197

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> With[{b = Coefficient[v, x, 1], d = Coefficient[u, x, 0],
e = Coefficient[u, x, 1], f = Coefficient[w, x, 0], g = Coefficient[w, x, 1]}, Simp[(g*u^(m + 1)*F^(c*v))/(b*c
*e*Log[F]), x] /; EqQ[e*g*(m + 1) - b*c*(e*f - d*g)*Log[F], 0]] /; FreeQ[{F, c, m}, x] && LinearQ[{u, v, w}, x
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {e^{-5+x} (-15+x)}{x^{16}} \, dx\\ &=\frac {e^{-5+x}}{3 x^{15}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{-5+x}}{3 x^{15}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-5 + x)*(-15 + x))/(3*x^16),x]

[Out]

E^(-5 + x)/(3*x^15)

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fricas [A]  time = 0.77, size = 10, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, e^{\left (x - 15 \, \log \relax (x) - 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(x-15)*exp(-15*log(x)+x-5)/x,x, algorithm="fricas")

[Out]

1/3*e^(x - 15*log(x) - 5)

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giac [A]  time = 0.16, size = 9, normalized size = 0.64 \begin {gather*} \frac {e^{\left (x - 5\right )}}{3 \, x^{15}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(x-15)*exp(-15*log(x)+x-5)/x,x, algorithm="giac")

[Out]

1/3*e^(x - 5)/x^15

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maple [A]  time = 0.06, size = 10, normalized size = 0.71

method	result	size
default	\(\frac {{\mathrm e}^{x -5}}{3 x^{15}}\)	\(10\)
risch	\(\frac {{\mathrm e}^{x -5}}{3 x^{15}}\)	\(10\)
gosper	\(\frac {{\mathrm e}^{-15 \ln \relax (x )+x -5}}{3}\)	\(11\)
norman	\(\frac {{\mathrm e}^{-15 \ln \relax (x )+x -5}}{3}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*(x-15)*exp(-15*ln(x)+x-5)/x,x,method=_RETURNVERBOSE)

[Out]

1/3/x^15*exp(x-5)

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maxima [C]  time = 0.37, size = 19, normalized size = 1.36 \begin {gather*} -\frac {1}{3} \, e^{\left (-5\right )} \Gamma \left (-14, -x\right ) - 5 \, e^{\left (-5\right )} \Gamma \left (-15, -x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(x-15)*exp(-15*log(x)+x-5)/x,x, algorithm="maxima")

[Out]

-1/3*e^(-5)*gamma(-14, -x) - 5*e^(-5)*gamma(-15, -x)

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mupad [B]  time = 5.49, size = 9, normalized size = 0.64 \begin {gather*} \frac {{\mathrm {e}}^{-5}\,{\mathrm {e}}^x}{3\,x^{15}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x - 15*log(x) - 5)*(x - 15))/(3*x),x)

[Out]

(exp(-5)*exp(x))/(3*x^15)

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sympy [A]  time = 0.11, size = 8, normalized size = 0.57 \begin {gather*} \frac {e^{x - 5}}{3 x^{15}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(x-15)*exp(-15*ln(x)+x-5)/x,x)

[Out]

exp(x - 5)/(3*x**15)

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