3.66.52 \(\int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx\)

Optimal. Leaf size=18 \[ \frac {3 \left (257-e^5+e^{16}+x\right )}{10 x} \]

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Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 30} \begin {gather*} \frac {3 \left (257-e^5+e^{16}\right )}{10 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-771 + 3*E^5 - 3*E^16)/(10*x^2),x]

[Out]

(3*(257 - E^5 + E^16))/(10*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} &=-\left (\frac {1}{10} \left (3 \left (257-e^5+e^{16}\right )\right ) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 \left (257-e^5+e^{16}\right )}{10 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} \frac {3 \left (257-e^5+e^{16}\right )}{10 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-771 + 3*E^5 - 3*E^16)/(10*x^2),x]

[Out]

(3*(257 - E^5 + E^16))/(10*x)

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fricas [A]  time = 0.93, size = 13, normalized size = 0.72 \begin {gather*} \frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-3*exp(16)+3*exp(5)-771)/x^2,x, algorithm="fricas")

[Out]

3/10*(e^16 - e^5 + 257)/x

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giac [A]  time = 0.19, size = 13, normalized size = 0.72 \begin {gather*} \frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-3*exp(16)+3*exp(5)-771)/x^2,x, algorithm="giac")

[Out]

3/10*(e^16 - e^5 + 257)/x

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maple [A]  time = 0.04, size = 14, normalized size = 0.78

method	result	size
gosper	\(-\frac {3 \left (-{\mathrm e}^{16}+{\mathrm e}^{5}-257\right )}{10 x}\)	\(14\)
norman	\(\frac {\frac {3 \,{\mathrm e}^{16}}{10}-\frac {3 \,{\mathrm e}^{5}}{10}+\frac {771}{10}}{x}\)	\(15\)
default	\(-\frac {-\frac {3 \,{\mathrm e}^{16}}{10}+\frac {3 \,{\mathrm e}^{5}}{10}-\frac {771}{10}}{x}\)	\(16\)
risch	\(\frac {3 \,{\mathrm e}^{16}}{10 x}-\frac {3 \,{\mathrm e}^{5}}{10 x}+\frac {771}{10 x}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/10*(-3*exp(16)+3*exp(5)-771)/x^2,x,method=_RETURNVERBOSE)

[Out]

-3/10*(-exp(16)+exp(5)-257)/x

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maxima [A]  time = 0.37, size = 13, normalized size = 0.72 \begin {gather*} \frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-3*exp(16)+3*exp(5)-771)/x^2,x, algorithm="maxima")

[Out]

3/10*(e^16 - e^5 + 257)/x

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mupad [B]  time = 4.07, size = 14, normalized size = 0.78 \begin {gather*} \frac {\frac {3\,{\mathrm {e}}^{16}}{10}-\frac {3\,{\mathrm {e}}^5}{10}+\frac {771}{10}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*exp(16))/10 - (3*exp(5))/10 + 771/10)/x^2,x)

[Out]

((3*exp(16))/10 - (3*exp(5))/10 + 771/10)/x

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sympy [A]  time = 0.06, size = 19, normalized size = 1.06 \begin {gather*} - \frac {- \frac {3 e^{16}}{10} - \frac {771}{10} + \frac {3 e^{5}}{10}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/10*(-3*exp(16)+3*exp(5)-771)/x**2,x)

[Out]

-(-3*exp(16)/10 - 771/10 + 3*exp(5)/10)/x

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