\(\int \frac {-768-30 x-12 \log (4)}{x^3} \, dx\) [9429]

Optimal result

Integrand size = 13, antiderivative size = 17 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=2+\frac {6 \left (5+\frac {64+\log (4)}{x}\right )}{x} \]

[Out]

6*((2*ln(2)+64)/x+5)/x+2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.47, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {37} \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {3 (5 x+2 (64+\log (4)))^2}{2 x^2 (64+\log (4))} \]

[In]

Int[(-768 - 30*x - 12*Log[4])/x^3,x]

[Out]

(3*(5*x + 2*(64 + Log[4]))^2)/(2*x^2*(64 + Log[4]))

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[(a + b*x)^(m + 1)*((c + d*x)^(n +
1)/((b*c - a*d)*(m + 1))), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rubi steps \begin{align*} \text {integral}& = \frac {3 (5 x+2 (64+\log (4)))^2}{2 x^2 (64+\log (4))} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {3 (128+10 x+\log (16))}{x^2} \]

[In]

Integrate[(-768 - 30*x - 12*Log[4])/x^3,x]

[Out]

(3*(128 + 10*x + Log[16]))/x^2

Maple [A] (verified)

Time = 0.11 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82

method	result	size
norman	\(\frac {30 x +12 \ln \left (2\right )+384}{x^{2}}\)	\(14\)
risch	\(\frac {30 x +12 \ln \left (2\right )+384}{x^{2}}\)	\(14\)
parallelrisch	\(\frac {30 x +12 \ln \left (2\right )+384}{x^{2}}\)	\(14\)
gosper	\(\frac {30 x +12 \ln \left (2\right )+384}{x^{2}}\)	\(15\)
default	\(\frac {30}{x}-\frac {3 \left (-4 \ln \left (2\right )-128\right )}{x^{2}}\)	\(18\)

[In]

int((-24*ln(2)-30*x-768)/x^3,x,method=_RETURNVERBOSE)

[Out]

(30*x+12*ln(2)+384)/x^2

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {6 \, {\left (5 \, x + 2 \, \log \left (2\right ) + 64\right )}}{x^{2}} \]

[In]

integrate((-24*log(2)-30*x-768)/x^3,x, algorithm="fricas")

[Out]

6*(5*x + 2*log(2) + 64)/x^2

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=- \frac {- 30 x - 384 - 12 \log {\left (2 \right )}}{x^{2}} \]

[In]

integrate((-24*ln(2)-30*x-768)/x**3,x)

[Out]

-(-30*x - 384 - 12*log(2))/x**2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {6 \, {\left (5 \, x + 2 \, \log \left (2\right ) + 64\right )}}{x^{2}} \]

[In]

integrate((-24*log(2)-30*x-768)/x^3,x, algorithm="maxima")

[Out]

6*(5*x + 2*log(2) + 64)/x^2

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {6 \, {\left (5 \, x + 2 \, \log \left (2\right ) + 64\right )}}{x^{2}} \]

[In]

integrate((-24*log(2)-30*x-768)/x^3,x, algorithm="giac")

[Out]

6*(5*x + 2*log(2) + 64)/x^2

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {-768-30 x-12 \log (4)}{x^3} \, dx=\frac {30\,x+12\,\ln \left (2\right )+384}{x^2} \]

[In]

int(-(30*x + 24*log(2) + 768)/x^3,x)

[Out]

(30*x + 12*log(2) + 384)/x^2