3.42.86 \(\int \frac {25-40 x+160 x^2-80 x^3+32 x^4+4 x^2 \log (5)}{25-320 x^2+80 x^3+1024 x^4-512 x^5+64 x^6+(-10 x+64 x^3-16 x^4) \log (5)+x^2 \log ^2(5)} \, dx\)

Optimal. Leaf size=31 \[ 5+\frac {-4+\frac {5}{x}}{8 (-4+x)-\frac {-\frac {5}{x}+\log (5)}{x}} \]

________________________________________________________________________________________

Rubi [F]  time = 180.02, 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 {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(25 - 40*x + 160*x^2 - 80*x^3 + 32*x^4 + 4*x^2*Log[5])/(25 - 320*x^2 + 80*x^3 + 1024*x^4 - 512*x^5 + 64*x^
6 + (-10*x + 64*x^3 - 16*x^4)*Log[5] + x^2*Log[5]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [A]  time = 0.02, size = 26, normalized size = 0.84 \begin {gather*} \frac {(5-4 x) x}{5-32 x^2+8 x^3-x \log (5)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(25 - 40*x + 160*x^2 - 80*x^3 + 32*x^4 + 4*x^2*Log[5])/(25 - 320*x^2 + 80*x^3 + 1024*x^4 - 512*x^5 +
64*x^6 + (-10*x + 64*x^3 - 16*x^4)*Log[5] + x^2*Log[5]^2),x]

[Out]

((5 - 4*x)*x)/(5 - 32*x^2 + 8*x^3 - x*Log[5])

________________________________________________________________________________________

fricas [A]  time = 0.93, size = 30, normalized size = 0.97 \begin {gather*} -\frac {4 \, x^{2} - 5 \, x}{8 \, x^{3} - 32 \, x^{2} - x \log \relax (5) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(5)+32*x^4-80*x^3+160*x^2-40*x+25)/(x^2*log(5)^2+(-16*x^4+64*x^3-10*x)*log(5)+64*x^6-512*x
^5+1024*x^4+80*x^3-320*x^2+25),x, algorithm="fricas")

[Out]

-(4*x^2 - 5*x)/(8*x^3 - 32*x^2 - x*log(5) + 5)

________________________________________________________________________________________

giac [A]  time = 0.13, size = 30, normalized size = 0.97 \begin {gather*} -\frac {4 \, x^{2} - 5 \, x}{8 \, x^{3} - 32 \, x^{2} - x \log \relax (5) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(5)+32*x^4-80*x^3+160*x^2-40*x+25)/(x^2*log(5)^2+(-16*x^4+64*x^3-10*x)*log(5)+64*x^6-512*x
^5+1024*x^4+80*x^3-320*x^2+25),x, algorithm="giac")

[Out]

-(4*x^2 - 5*x)/(8*x^3 - 32*x^2 - x*log(5) + 5)

________________________________________________________________________________________

maple [A]  time = 0.08, size = 26, normalized size = 0.84

method	result	size
gosper	\(\frac {x \left (4 x -5\right )}{-8 x^{3}+x \ln \relax (5)+32 x^{2}-5}\)	\(26\)
default	\(\frac {4 x^{2}-5 x}{-8 x^{3}+x \ln \relax (5)+32 x^{2}-5}\)	\(29\)
norman	\(\frac {4 x^{2}-5 x}{-8 x^{3}+x \ln \relax (5)+32 x^{2}-5}\)	\(29\)
risch	\(\frac {4 x^{2}-5 x}{-8 x^{3}+x \ln \relax (5)+32 x^{2}-5}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^2*ln(5)+32*x^4-80*x^3+160*x^2-40*x+25)/(x^2*ln(5)^2+(-16*x^4+64*x^3-10*x)*ln(5)+64*x^6-512*x^5+1024*x
^4+80*x^3-320*x^2+25),x,method=_RETURNVERBOSE)

[Out]

x*(4*x-5)/(-8*x^3+x*ln(5)+32*x^2-5)

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 30, normalized size = 0.97 \begin {gather*} -\frac {4 \, x^{2} - 5 \, x}{8 \, x^{3} - 32 \, x^{2} - x \log \relax (5) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^2*log(5)+32*x^4-80*x^3+160*x^2-40*x+25)/(x^2*log(5)^2+(-16*x^4+64*x^3-10*x)*log(5)+64*x^6-512*x
^5+1024*x^4+80*x^3-320*x^2+25),x, algorithm="maxima")

[Out]

-(4*x^2 - 5*x)/(8*x^3 - 32*x^2 - x*log(5) + 5)

________________________________________________________________________________________

mupad [B]  time = 0.11, size = 25, normalized size = 0.81 \begin {gather*} \frac {x\,\left (4\,x-5\right )}{-8\,x^3+32\,x^2+\ln \relax (5)\,x-5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^2*log(5) - 40*x + 160*x^2 - 80*x^3 + 32*x^4 + 25)/(x^2*log(5)^2 - log(5)*(10*x - 64*x^3 + 16*x^4) - 3
20*x^2 + 80*x^3 + 1024*x^4 - 512*x^5 + 64*x^6 + 25),x)

[Out]

(x*(4*x - 5))/(x*log(5) + 32*x^2 - 8*x^3 - 5)

________________________________________________________________________________________

sympy [A]  time = 1.18, size = 24, normalized size = 0.77 \begin {gather*} \frac {- 4 x^{2} + 5 x}{8 x^{3} - 32 x^{2} - x \log {\relax (5 )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**2*ln(5)+32*x**4-80*x**3+160*x**2-40*x+25)/(x**2*ln(5)**2+(-16*x**4+64*x**3-10*x)*ln(5)+64*x**6
-512*x**5+1024*x**4+80*x**3-320*x**2+25),x)

[Out]

(-4*x**2 + 5*x)/(8*x**3 - 32*x**2 - x*log(5) + 5)

________________________________________________________________________________________