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

Optimal. Leaf size=17 \[ 2+\frac {6 \left (5+\frac {64+\log (4)}{x}\right )}{x} \]

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Rubi [A]  time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.47, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {37} \begin {gather*} \frac {3 (5 x+2 (64+\log (4)))^2}{2 x^2 (64+\log (4))} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=\frac {3 (5 x+2 (64+\log (4)))^2}{2 x^2 (64+\log (4))}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.71 \begin {gather*} \frac {3 (128+10 x+\log (16))}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(3*(128 + 10*x + Log[16]))/x^2

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fricas [A]  time = 0.51, size = 14, normalized size = 0.82 \begin {gather*} \frac {6 \, {\left (5 \, x + 2 \, \log \relax (2) + 64\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*(5*x + 2*log(2) + 64)/x^2

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giac [A]  time = 0.27, size = 14, normalized size = 0.82 \begin {gather*} \frac {6 \, {\left (5 \, x + 2 \, \log \relax (2) + 64\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*(5*x + 2*log(2) + 64)/x^2

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maple [A]  time = 0.04, size = 14, normalized size = 0.82

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} \frac {6 \, {\left (5 \, x + 2 \, \log \relax (2) + 64\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*(5*x + 2*log(2) + 64)/x^2

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mupad [B]  time = 0.05, size = 13, normalized size = 0.76 \begin {gather*} \frac {30\,x+12\,\ln \relax (2)+384}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(30*x + 24*log(2) + 768)/x^3,x)

[Out]

(30*x + 12*log(2) + 384)/x^2

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sympy [A]  time = 0.14, size = 15, normalized size = 0.88 \begin {gather*} - \frac {- 30 x - 384 - 12 \log {\relax (2 )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(-30*x - 384 - 12*log(2))/x**2

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