\(\int \frac {-16-4 \log (2)}{x^5} \, dx\) [7598]

Optimal result

Integrand size = 10, antiderivative size = 8 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {4+\log (2)}{x^4} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {4+\log (2)}{x^4} \]

[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{align*} \text {integral}& = -\left ((16+4 \log (2)) \int \frac {1}{x^5} \, dx\right ) \\ & = \frac {4+\log (2)}{x^4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {4+\log (2)}{x^4} \]

[In]

Integrate[(-16 - 4*Log[2])/x^5,x]

[Out]

(4 + Log[2])/x^4

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {\log \left (2\right ) + 4}{x^{4}} \]

[In]

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

[Out]

(log(2) + 4)/x^4

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.75 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=- \frac {-16 - 4 \log {\left (2 \right )}}{4 x^{4}} \]

[In]

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

[Out]

-(-16 - 4*log(2))/(4*x**4)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {\log \left (2\right ) + 4}{x^{4}} \]

[In]

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

[Out]

(log(2) + 4)/x^4

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {\log \left (2\right ) + 4}{x^{4}} \]

[In]

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

[Out]

(log(2) + 4)/x^4

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {-16-4 \log (2)}{x^5} \, dx=\frac {\ln \left (2\right )+4}{x^4} \]

[In]

int(-(4*log(2) + 16)/x^5,x)

[Out]

(log(2) + 4)/x^4