\(\int -\frac {388129 \log (5)}{32 x^2} \, dx\) [1094]

Optimal result

Integrand size = 9, antiderivative size = 14 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=2+\frac {x+\frac {388129 \log (5)}{32}}{x} \]

[Out]

2+(x+388129/32*ln(5))/x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30} \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \log (5)}{32 x} \]

[In]

Int[(-388129*Log[5])/(32*x^2),x]

[Out]

(388129*Log[5])/(32*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{align*} \text {integral}& = -\left (\frac {1}{32} (388129 \log (5)) \int \frac {1}{x^2} \, dx\right ) \\ & = \frac {388129 \log (5)}{32 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \log (5)}{32 x} \]

[In]

Integrate[(-388129*Log[5])/(32*x^2),x]

[Out]

(388129*Log[5])/(32*x)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57

method	result	size
gosper	\(\frac {388129 \ln \left (5\right )}{32 x}\)	\(8\)
default	\(\frac {388129 \ln \left (5\right )}{32 x}\)	\(8\)
norman	\(\frac {388129 \ln \left (5\right )}{32 x}\)	\(8\)
risch	\(\frac {388129 \ln \left (5\right )}{32 x}\)	\(8\)
parallelrisch	\(\frac {388129 \ln \left (5\right )}{32 x}\)	\(8\)

[In]

int(-388129/32*ln(5)/x^2,x,method=_RETURNVERBOSE)

[Out]

388129/32*ln(5)/x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \, \log \left (5\right )}{32 \, x} \]

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="fricas")

[Out]

388129/32*log(5)/x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \log {\left (5 \right )}}{32 x} \]

[In]

integrate(-388129/32*ln(5)/x**2,x)

[Out]

388129*log(5)/(32*x)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \, \log \left (5\right )}{32 \, x} \]

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="maxima")

[Out]

388129/32*log(5)/x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129 \, \log \left (5\right )}{32 \, x} \]

[In]

integrate(-388129/32*log(5)/x^2,x, algorithm="giac")

[Out]

388129/32*log(5)/x

Mupad [B] (verification not implemented)

Time = 8.58 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -\frac {388129 \log (5)}{32 x^2} \, dx=\frac {388129\,\ln \left (5\right )}{32\,x} \]

[In]

int(-(388129*log(5))/(32*x^2),x)

[Out]

(388129*log(5))/(32*x)