3.76.98 \(\int \frac {-16-4 \log (2)}{x^5} \, dx\)

Optimal. Leaf size=8 \[ \frac {4+\log (2)}{x^4} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, 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 {4+\log (2)}{x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-16 - 4*Log[2])/x^5,x]

[Out]

(4 + Log[2])/x^4

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 ((16+4 \log (2)) \int \frac {1}{x^5} \, dx\right )\\ &=\frac {4+\log (2)}{x^4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {4+\log (2)}{x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16 - 4*Log[2])/x^5,x]

[Out]

(4 + Log[2])/x^4

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fricas [A]  time = 0.85, size = 8, normalized size = 1.00 \begin {gather*} \frac {\log \relax (2) + 4}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(2)-16)/x^5,x, algorithm="fricas")

[Out]

(log(2) + 4)/x^4

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giac [A]  time = 0.14, size = 8, normalized size = 1.00 \begin {gather*} \frac {\log \relax (2) + 4}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(2)-16)/x^5,x, algorithm="giac")

[Out]

(log(2) + 4)/x^4

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maple [A]  time = 0.02, size = 9, normalized size = 1.12

method	result	size
gosper	\(\frac {4+\ln \relax (2)}{x^{4}}\)	\(9\)
norman	\(\frac {4+\ln \relax (2)}{x^{4}}\)	\(9\)
default	\(-\frac {-4 \ln \relax (2)-16}{4 x^{4}}\)	\(12\)
risch	\(\frac {\ln \relax (2)}{x^{4}}+\frac {4}{x^{4}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*ln(2)-16)/x^5,x,method=_RETURNVERBOSE)

[Out]

1/x^4*(4+ln(2))

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maxima [A]  time = 0.35, size = 8, normalized size = 1.00 \begin {gather*} \frac {\log \relax (2) + 4}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*log(2)-16)/x^5,x, algorithm="maxima")

[Out]

(log(2) + 4)/x^4

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mupad [B]  time = 0.04, size = 8, normalized size = 1.00 \begin {gather*} \frac {\ln \relax (2)+4}{x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*log(2) + 16)/x^5,x)

[Out]

(log(2) + 4)/x^4

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sympy [A]  time = 0.05, size = 14, normalized size = 1.75 \begin {gather*} - \frac {-16 - 4 \log {\relax (2 )}}{4 x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*ln(2)-16)/x**5,x)

[Out]

-(-16 - 4*log(2))/(4*x**4)

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