3.35.20 \(\int \frac {(1-4 x-1083 x^2-608 x^3-80 x^4) \log (4)}{x^2-4 x^3-718 x^4+1140 x^5+130897 x^6+109808 x^7+34656 x^8+4864 x^9+256 x^{10}} \, dx\)

Optimal. Leaf size=23 \[ \frac {\log (4)}{x \left (-1+2 x+(x-4 x (5+x))^2\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 0.59, 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*} \int \frac {\left (1-4 x-1083 x^2-608 x^3-80 x^4\right ) \log (4)}{x^2-4 x^3-718 x^4+1140 x^5+130897 x^6+109808 x^7+34656 x^8+4864 x^9+256 x^{10}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((1 - 4*x - 1083*x^2 - 608*x^3 - 80*x^4)*Log[4])/(x^2 - 4*x^3 - 718*x^4 + 1140*x^5 + 130897*x^6 + 109808*x
^7 + 34656*x^8 + 4864*x^9 + 256*x^10),x]

[Out]

-(Log[4]/x) - Log[4]/(2*(1 - 2*x - 361*x^2 - 152*x^3 - 16*x^4)) - 725*Log[4]*Defer[Int][(-1 + 2*x + 361*x^2 +
152*x^3 + 16*x^4)^(-2), x] - 817*Log[4]*Defer[Int][x/(-1 + 2*x + 361*x^2 + 152*x^3 + 16*x^4)^2, x] - 140*Log[4
]*Defer[Int][x^2/(-1 + 2*x + 361*x^2 + 152*x^3 + 16*x^4)^2, x] - 361*Log[4]*Defer[Int][(-1 + 2*x + 361*x^2 + 1
52*x^3 + 16*x^4)^(-1), x] - 152*Log[4]*Defer[Int][x/(-1 + 2*x + 361*x^2 + 152*x^3 + 16*x^4), x] - 16*Log[4]*De
fer[Int][x^2/(-1 + 2*x + 361*x^2 + 152*x^3 + 16*x^4), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log (4) \int \frac {1-4 x-1083 x^2-608 x^3-80 x^4}{x^2-4 x^3-718 x^4+1140 x^5+130897 x^6+109808 x^7+34656 x^8+4864 x^9+256 x^{10}} \, dx\\ &=\log (4) \int \left (\frac {1}{x^2}-\frac {2 \left (363+589 x+184 x^2+16 x^3\right )}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2}-\frac {(19+4 x)^2}{-1+2 x+361 x^2+152 x^3+16 x^4}\right ) \, dx\\ &=-\frac {\log (4)}{x}-\log (4) \int \frac {(19+4 x)^2}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(2 \log (4)) \int \frac {363+589 x+184 x^2+16 x^3}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2} \, dx\\ &=-\frac {\log (4)}{x}-\frac {\log (4)}{2 \left (1-2 x-361 x^2-152 x^3-16 x^4\right )}-\frac {1}{32} \log (4) \int \frac {23200+26144 x+4480 x^2}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2} \, dx-\log (4) \int \left (\frac {361}{-1+2 x+361 x^2+152 x^3+16 x^4}+\frac {152 x}{-1+2 x+361 x^2+152 x^3+16 x^4}+\frac {16 x^2}{-1+2 x+361 x^2+152 x^3+16 x^4}\right ) \, dx\\ &=-\frac {\log (4)}{x}-\frac {\log (4)}{2 \left (1-2 x-361 x^2-152 x^3-16 x^4\right )}-\frac {1}{32} \log (4) \int \left (\frac {23200}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2}+\frac {26144 x}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2}+\frac {4480 x^2}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2}\right ) \, dx-(16 \log (4)) \int \frac {x^2}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(152 \log (4)) \int \frac {x}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(361 \log (4)) \int \frac {1}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx\\ &=-\frac {\log (4)}{x}-\frac {\log (4)}{2 \left (1-2 x-361 x^2-152 x^3-16 x^4\right )}-(16 \log (4)) \int \frac {x^2}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(140 \log (4)) \int \frac {x^2}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2} \, dx-(152 \log (4)) \int \frac {x}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(361 \log (4)) \int \frac {1}{-1+2 x+361 x^2+152 x^3+16 x^4} \, dx-(725 \log (4)) \int \frac {1}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2} \, dx-(817 \log (4)) \int \frac {x}{\left (-1+2 x+361 x^2+152 x^3+16 x^4\right )^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.02, size = 28, normalized size = 1.22 \begin {gather*} -\frac {\log (4)}{x-2 x^2-361 x^3-152 x^4-16 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((1 - 4*x - 1083*x^2 - 608*x^3 - 80*x^4)*Log[4])/(x^2 - 4*x^3 - 718*x^4 + 1140*x^5 + 130897*x^6 + 10
9808*x^7 + 34656*x^8 + 4864*x^9 + 256*x^10),x]

[Out]

-(Log[4]/(x - 2*x^2 - 361*x^3 - 152*x^4 - 16*x^5))

________________________________________________________________________________________

fricas [A]  time = 0.90, size = 30, normalized size = 1.30 \begin {gather*} \frac {2 \, \log \relax (2)}{16 \, x^{5} + 152 \, x^{4} + 361 \, x^{3} + 2 \, x^{2} - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-80*x^4-608*x^3-1083*x^2-4*x+1)*log(2)/(256*x^10+4864*x^9+34656*x^8+109808*x^7+130897*x^6+1140*x^
5-718*x^4-4*x^3+x^2),x, algorithm="fricas")

[Out]

2*log(2)/(16*x^5 + 152*x^4 + 361*x^3 + 2*x^2 - x)

________________________________________________________________________________________

giac [A]  time = 0.17, size = 30, normalized size = 1.30 \begin {gather*} \frac {2 \, \log \relax (2)}{16 \, x^{5} + 152 \, x^{4} + 361 \, x^{3} + 2 \, x^{2} - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-80*x^4-608*x^3-1083*x^2-4*x+1)*log(2)/(256*x^10+4864*x^9+34656*x^8+109808*x^7+130897*x^6+1140*x^
5-718*x^4-4*x^3+x^2),x, algorithm="giac")

[Out]

2*log(2)/(16*x^5 + 152*x^4 + 361*x^3 + 2*x^2 - x)

________________________________________________________________________________________

maple [A]  time = 0.04, size = 30, normalized size = 1.30

method	result	size
gosper	\(\frac {2 \ln \relax (2)}{x \left (16 x^{4}+152 x^{3}+361 x^{2}+2 x -1\right )}\)	\(30\)
norman	\(\frac {2 \ln \relax (2)}{x \left (16 x^{4}+152 x^{3}+361 x^{2}+2 x -1\right )}\)	\(30\)
risch	\(\frac {2 \ln \relax (2)}{x \left (16 x^{4}+152 x^{3}+361 x^{2}+2 x -1\right )}\)	\(30\)
default	\(2 \ln \relax (2) \left (-\frac {-x^{3}-\frac {19}{2} x^{2}-\frac {361}{16} x -\frac {1}{8}}{x^{4}+\frac {19}{2} x^{3}+\frac {361}{16} x^{2}+\frac {1}{8} x -\frac {1}{16}}-\frac {1}{x}\right )\)	\(48\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*(-80*x^4-608*x^3-1083*x^2-4*x+1)*ln(2)/(256*x^10+4864*x^9+34656*x^8+109808*x^7+130897*x^6+1140*x^5-718*x
^4-4*x^3+x^2),x,method=_RETURNVERBOSE)

[Out]

2/x*ln(2)/(16*x^4+152*x^3+361*x^2+2*x-1)

________________________________________________________________________________________

maxima [A]  time = 0.45, size = 30, normalized size = 1.30 \begin {gather*} \frac {2 \, \log \relax (2)}{16 \, x^{5} + 152 \, x^{4} + 361 \, x^{3} + 2 \, x^{2} - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-80*x^4-608*x^3-1083*x^2-4*x+1)*log(2)/(256*x^10+4864*x^9+34656*x^8+109808*x^7+130897*x^6+1140*x^
5-718*x^4-4*x^3+x^2),x, algorithm="maxima")

[Out]

2*log(2)/(16*x^5 + 152*x^4 + 361*x^3 + 2*x^2 - x)

________________________________________________________________________________________

mupad [B]  time = 0.13, size = 29, normalized size = 1.26 \begin {gather*} \frac {2\,\ln \relax (2)}{x\,\left (16\,x^4+152\,x^3+361\,x^2+2\,x-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*log(2)*(4*x + 1083*x^2 + 608*x^3 + 80*x^4 - 1))/(x^2 - 4*x^3 - 718*x^4 + 1140*x^5 + 130897*x^6 + 10980
8*x^7 + 34656*x^8 + 4864*x^9 + 256*x^10),x)

[Out]

(2*log(2))/(x*(2*x + 361*x^2 + 152*x^3 + 16*x^4 - 1))

________________________________________________________________________________________

sympy [A]  time = 0.46, size = 26, normalized size = 1.13 \begin {gather*} \frac {2 \log {\relax (2 )}}{16 x^{5} + 152 x^{4} + 361 x^{3} + 2 x^{2} - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-80*x**4-608*x**3-1083*x**2-4*x+1)*ln(2)/(256*x**10+4864*x**9+34656*x**8+109808*x**7+130897*x**6+
1140*x**5-718*x**4-4*x**3+x**2),x)

[Out]

2*log(2)/(16*x**5 + 152*x**4 + 361*x**3 + 2*x**2 - x)

________________________________________________________________________________________