3.16.57 \(\int \frac {32 e^8}{x^3} \, dx\)

Optimal. Leaf size=10 \[ 1-\frac {16 e^8}{x^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} -\frac {16 e^8}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(32*E^8)/x^3,x]

[Out]

(-16*E^8)/x^2

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 (32 e^8\right ) \int \frac {1}{x^3} \, dx\\ &=-\frac {16 e^8}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.80 \begin {gather*} -\frac {16 e^8}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(32*E^8)/x^3,x]

[Out]

(-16*E^8)/x^2

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fricas [A]  time = 1.17, size = 7, normalized size = 0.70 \begin {gather*} -\frac {16 \, e^{8}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*exp(2)^4/x^3,x, algorithm="fricas")

[Out]

-16*e^8/x^2

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giac [A]  time = 0.15, size = 7, normalized size = 0.70 \begin {gather*} -\frac {16 \, e^{8}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*exp(2)^4/x^3,x, algorithm="giac")

[Out]

-16*e^8/x^2

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maple [A]  time = 0.02, size = 8, normalized size = 0.80

method	result	size
risch	\(-\frac {16 \,{\mathrm e}^{8}}{x^{2}}\)	\(8\)
gosper	\(-\frac {16 \,{\mathrm e}^{8}}{x^{2}}\)	\(10\)
default	\(-\frac {16 \,{\mathrm e}^{8}}{x^{2}}\)	\(10\)
norman	\(-\frac {16 \,{\mathrm e}^{8}}{x^{2}}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*exp(2)^4/x^3,x,method=_RETURNVERBOSE)

[Out]

-16/x^2*exp(8)

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maxima [A]  time = 0.37, size = 7, normalized size = 0.70 \begin {gather*} -\frac {16 \, e^{8}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*exp(2)^4/x^3,x, algorithm="maxima")

[Out]

-16*e^8/x^2

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mupad [B]  time = 0.97, size = 7, normalized size = 0.70 \begin {gather*} -\frac {16\,{\mathrm {e}}^8}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((32*exp(8))/x^3,x)

[Out]

-(16*exp(8))/x^2

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sympy [A]  time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} - \frac {16 e^{8}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*exp(2)**4/x**3,x)

[Out]

-16*exp(8)/x**2

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