3.73.76 $\int \frac{-6+4x-24x^2+16x^3}{(-5+24x-40x^2+16x^3+16x^4)\log (\frac{5-14x+12x^2+8x^3}{1-4x+4x^2})}dx$

Optimal. Leaf size=27 $$1+e^2+\log (\log (5+2x+\frac{x}{{(2(\frac{1}{4}-x)+x)}^2}))$$

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Rubi [F]  time = 0.73, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{-6+4x-24x^2+16x^3}{(-5+24x-40x^2+16x^3+16x^4)\log \left(\frac{5-14x+12x^2+8x^3}{1-4x+4x^2}\right)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-6 + 4*x - 24*x^2 + 16*x^3)/((-5 + 24*x - 40*x^2 + 16*x^3 + 16*x^4)*Log[(5 - 14*x + 12*x^2 + 8*x^3)/(1 -
4*x + 4*x^2)]),x]

[Out]

-4*Defer[Int][1/((-1 + 2*x)*Log[(5 - 14*x + 12*x^2 + 8*x^3)/(-1 + 2*x)^2]), x] - 14*Defer[Int][1/((5 - 14*x +
12*x^2 + 8*x^3)*Log[(5 - 14*x + 12*x^2 + 8*x^3)/(-1 + 2*x)^2]), x] + 24*Defer[Int][x/((5 - 14*x + 12*x^2 + 8*x
^3)*Log[(5 - 14*x + 12*x^2 + 8*x^3)/(-1 + 2*x)^2]), x] + 24*Defer[Int][x^2/((5 - 14*x + 12*x^2 + 8*x^3)*Log[(5
- 14*x + 12*x^2 + 8*x^3)/(-1 + 2*x)^2]), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-\frac{4}{(-1+2x)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}+\frac{2(-7+12x+12x^2)}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)})dx\\ & =2\int \frac{-7+12x+12x^2}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx-4\int \frac{1}{(-1+2x)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx\\ & =2\int (-\frac{7}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}+\frac{12x}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}+\frac{12x^2}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)})dx-4\int \frac{1}{(-1+2x)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx\\ & =-(4\int \frac{1}{(-1+2x)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx)-14\int \frac{1}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx+24\int \frac{x}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx+24\int \frac{x^2}{(5-14x+12x^2+8x^3)\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right)}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.15, size = 25, normalized size = 0.93 $$\begin{array}{c}\log (\log \left(\frac{5-14x+12x^2+8x^3}{(-1+2x{)}^2}\right))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-6 + 4*x - 24*x^2 + 16*x^3)/((-5 + 24*x - 40*x^2 + 16*x^3 + 16*x^4)*Log[(5 - 14*x + 12*x^2 + 8*x^3)
/(1 - 4*x + 4*x^2)]),x]

[Out]

Log[Log[(5 - 14*x + 12*x^2 + 8*x^3)/(-1 + 2*x)^2]]

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fricas [A]  time = 0.58, size = 30, normalized size = 1.11 $$\begin{array}{c}\log (\log \left(\frac{8x^3+12x^2-14x+5}{4x^2-4x+1}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3-24*x^2+4*x-6)/(16*x^4+16*x^3-40*x^2+24*x-5)/log((8*x^3+12*x^2-14*x+5)/(4*x^2-4*x+1)),x, algo
rithm="fricas")

[Out]

log(log((8*x^3 + 12*x^2 - 14*x + 5)/(4*x^2 - 4*x + 1)))

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giac [A]  time = 0.21, size = 30, normalized size = 1.11 $$\begin{array}{c}\log (\log \left(\frac{8x^3+12x^2-14x+5}{4x^2-4x+1}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3-24*x^2+4*x-6)/(16*x^4+16*x^3-40*x^2+24*x-5)/log((8*x^3+12*x^2-14*x+5)/(4*x^2-4*x+1)),x, algo
rithm="giac")

[Out]

log(log((8*x^3 + 12*x^2 - 14*x + 5)/(4*x^2 - 4*x + 1)))

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maple [A]  time = 0.04, size = 31, normalized size = 1.15

method	result	size
norman	$\ln (\ln \left(\frac{8x^3+12x^2-14x+5}{4x^2-4x+1}\right))$	$31$
risch	$\ln (\ln \left(\frac{8x^3+12x^2-14x+5}{4x^2-4x+1}\right))$	$31$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x^3-24*x^2+4*x-6)/(16*x^4+16*x^3-40*x^2+24*x-5)/ln((8*x^3+12*x^2-14*x+5)/(4*x^2-4*x+1)),x,method=_RETU
RNVERBOSE)

[Out]

ln(ln((8*x^3+12*x^2-14*x+5)/(4*x^2-4*x+1)))

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maxima [A]  time = 0.41, size = 26, normalized size = 0.96 $$\begin{array}{c}\log (\log (8x^3+12x^2-14x+5)-2\log (2x-1))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3-24*x^2+4*x-6)/(16*x^4+16*x^3-40*x^2+24*x-5)/log((8*x^3+12*x^2-14*x+5)/(4*x^2-4*x+1)),x, algo
rithm="maxima")

[Out]

log(log(8*x^3 + 12*x^2 - 14*x + 5) - 2*log(2*x - 1))

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mupad [B]  time = 4.88, size = 22, normalized size = 0.81 $$\begin{array}{c}\ln (\ln (2x+\frac{4x}{4x^2-4x+1}+5))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x - 24*x^2 + 16*x^3 - 6)/(log((12*x^2 - 14*x + 8*x^3 + 5)/(4*x^2 - 4*x + 1))*(24*x - 40*x^2 + 16*x^3 +
16*x^4 - 5)),x)

[Out]

log(log(2*x + (4*x)/(4*x^2 - 4*x + 1) + 5))

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sympy [A]  time = 0.34, size = 27, normalized size = 1.00 $$\begin{array}{c}\log (\log \left(\frac{8x^3+12x^2-14x+5}{4x^2-4x+1}\right))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x**3-24*x**2+4*x-6)/(16*x**4+16*x**3-40*x**2+24*x-5)/ln((8*x**3+12*x**2-14*x+5)/(4*x**2-4*x+1)),
x)

[Out]

log(log((8*x**3 + 12*x**2 - 14*x + 5)/(4*x**2 - 4*x + 1)))

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