3.91.72 \(\int \frac {-3 x-8 x^2+x^3-8 x^4-x^5+(-6 x^2+3 x^3) \log (2)+(45+15 x+30 x^3+10 x^4) \log (3+x)}{270-90 x-30 x^2-170 x^3+20 x^5+30 x^6+10 x^7+(-540 x+60 x^3+180 x^4+60 x^5) \log (2)+(270 x^2+90 x^3) \log ^2(2)} \, dx\) [9072]

Optimal. Leaf size=32 \[ \frac {-\frac {x}{5}+\log (3+x)}{2 \left (-1+\frac {3}{x}-x^2-3 \log (2)\right )} \]

[Out]

1/2*(ln(3+x)-1/5*x)/(3/x-3*ln(2)-1-x^2)

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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[(-3*x - 8*x^2 + x^3 - 8*x^4 - x^5 + (-6*x^2 + 3*x^3)*Log[2] + (45 + 15*x + 30*x^3 + 10*x^4)*Log[3 + x])/(2
70 - 90*x - 30*x^2 - 170*x^3 + 20*x^5 + 30*x^6 + 10*x^7 + (-540*x + 60*x^3 + 180*x^4 + 60*x^5)*Log[2] + (270*x
^2 + 90*x^3)*Log[2]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(32)=64\).
time = 0.74, size = 113, normalized size = 3.53 \begin {gather*} \frac {x \left (x \left (2717+68 \log ^3(8)+4 \log ^4(8)+\log (8) (319-3 \log (64))-6 \log ^2(8) (-25+\log (64))+30 \log (64)\right )-5 \left (2717+379 \log (8)+144 \log ^2(8)+56 \log ^3(8)+4 \log ^4(8)\right ) \log (3+x)\right )}{10 (11+\log (8)) \left (-3+x+x^3+x \log (8)\right ) \left (247+12 \log (8)+12 \log ^2(8)+4 \log ^3(8)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3*x - 8*x^2 + x^3 - 8*x^4 - x^5 + (-6*x^2 + 3*x^3)*Log[2] + (45 + 15*x + 30*x^3 + 10*x^4)*Log[3 +
x])/(270 - 90*x - 30*x^2 - 170*x^3 + 20*x^5 + 30*x^6 + 10*x^7 + (-540*x + 60*x^3 + 180*x^4 + 60*x^5)*Log[2] +
(270*x^2 + 90*x^3)*Log[2]^2),x]

[Out]

(x*(x*(2717 + 68*Log[8]^3 + 4*Log[8]^4 + Log[8]*(319 - 3*Log[64]) - 6*Log[8]^2*(-25 + Log[64]) + 30*Log[64]) -
5*(2717 + 379*Log[8] + 144*Log[8]^2 + 56*Log[8]^3 + 4*Log[8]^4)*Log[3 + x]))/(10*(11 + Log[8])*(-3 + x + x^3
+ x*Log[8])*(247 + 12*Log[8] + 12*Log[8]^2 + 4*Log[8]^3))

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(340\) vs. \(2(28)=56\).
time = 1.22, size = 341, normalized size = 10.66

method	result	size
norman	\(\frac {-\frac {x \ln \left (3+x \right )}{2}+\frac {x^{2}}{10}}{x^{3}+3 x \ln \left (2\right )+x -3}\)	\(28\)
risch	\(-\frac {x \ln \left (3+x \right )}{2 \left (x^{3}+3 x \ln \left (2\right )+x -3\right )}+\frac {x^{2}}{10 x^{3}+30 x \ln \left (2\right )+10 x -30}\)	\(40\)
derivativedivides	\(-\frac {\ln \left (3+x \right )}{2 \left (3 \ln \left (2\right )+11\right )}+\frac {\ln \left (2\right ) \left (3+x \right )^{2}}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {11 \left (3+x \right )^{2}}{30 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}-\frac {3 \ln \left (2\right ) \left (3+x \right )}{5 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}-\frac {11 \left (3+x \right )}{5 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {9 \ln \left (2\right )}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {33}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {\ln \left (3+x \right ) \left (3+x \right ) \left (\left (3+x \right )^{2}-10-9 x \right )}{2 \left (\left (3+x \right )^{3}+3 \left (3+x \right ) \ln \left (2\right )-9 \left (3+x \right )^{2}-9 \ln \left (2\right )+51+28 x \right ) \left (3 \ln \left (2\right )+11\right )}\)	\(341\)
default	\(-\frac {\ln \left (3+x \right )}{2 \left (3 \ln \left (2\right )+11\right )}+\frac {\ln \left (2\right ) \left (3+x \right )^{2}}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {11 \left (3+x \right )^{2}}{30 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}-\frac {3 \ln \left (2\right ) \left (3+x \right )}{5 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}-\frac {11 \left (3+x \right )}{5 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {9 \ln \left (2\right )}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {33}{10 \left (3 \ln \left (2\right )+11\right ) \left (\frac {\left (3+x \right )^{3}}{3}+\left (3+x \right ) \ln \left (2\right )-3 \left (3+x \right )^{2}-3 \ln \left (2\right )+17+\frac {28 x}{3}\right )}+\frac {\ln \left (3+x \right ) \left (3+x \right ) \left (\left (3+x \right )^{2}-10-9 x \right )}{2 \left (\left (3+x \right )^{3}+3 \left (3+x \right ) \ln \left (2\right )-9 \left (3+x \right )^{2}-9 \ln \left (2\right )+51+28 x \right ) \left (3 \ln \left (2\right )+11\right )}\)	\(341\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((10*x^4+30*x^3+15*x+45)*ln(3+x)+(3*x^3-6*x^2)*ln(2)-x^5-8*x^4+x^3-8*x^2-3*x)/((90*x^3+270*x^2)*ln(2)^2+(6
0*x^5+180*x^4+60*x^3-540*x)*ln(2)+10*x^7+30*x^6+20*x^5-170*x^3-30*x^2-90*x+270),x,method=_RETURNVERBOSE)

[Out]

-1/2/(3*ln(2)+11)*ln(3+x)+1/10/(3*ln(2)+11)/(1/3*(3+x)^3+(3+x)*ln(2)-3*(3+x)^2-3*ln(2)+17+28/3*x)*ln(2)*(3+x)^
2+11/30/(3*ln(2)+11)/(1/3*(3+x)^3+(3+x)*ln(2)-3*(3+x)^2-3*ln(2)+17+28/3*x)*(3+x)^2-3/5/(3*ln(2)+11)/(1/3*(3+x)
^3+(3+x)*ln(2)-3*(3+x)^2-3*ln(2)+17+28/3*x)*ln(2)*(3+x)-11/5/(3*ln(2)+11)/(1/3*(3+x)^3+(3+x)*ln(2)-3*(3+x)^2-3
*ln(2)+17+28/3*x)*(3+x)+9/10/(3*ln(2)+11)/(1/3*(3+x)^3+(3+x)*ln(2)-3*(3+x)^2-3*ln(2)+17+28/3*x)*ln(2)+33/10/(3
*ln(2)+11)/(1/3*(3+x)^3+(3+x)*ln(2)-3*(3+x)^2-3*ln(2)+17+28/3*x)+1/2*ln(3+x)*(3+x)*((3+x)^2-10-9*x)/((3+x)^3+3
*(3+x)*ln(2)-9*(3+x)^2-9*ln(2)+51+28*x)/(3*ln(2)+11)

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Maxima [A]
time = 0.49, size = 28, normalized size = 0.88 \begin {gather*} \frac {x^{2} - 5 \, x \log \left (x + 3\right )}{10 \, {\left (x^{3} + x {\left (3 \, \log \left (2\right ) + 1\right )} - 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4+30*x^3+15*x+45)*log(3+x)+(3*x^3-6*x^2)*log(2)-x^5-8*x^4+x^3-8*x^2-3*x)/((90*x^3+270*x^2)*lo
g(2)^2+(60*x^5+180*x^4+60*x^3-540*x)*log(2)+10*x^7+30*x^6+20*x^5-170*x^3-30*x^2-90*x+270),x, algorithm="maxima
")

[Out]

1/10*(x^2 - 5*x*log(x + 3))/(x^3 + x*(3*log(2) + 1) - 3)

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Fricas [A]
time = 0.40, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^{2} - 5 \, x \log \left (x + 3\right )}{10 \, {\left (x^{3} + 3 \, x \log \left (2\right ) + x - 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4+30*x^3+15*x+45)*log(3+x)+(3*x^3-6*x^2)*log(2)-x^5-8*x^4+x^3-8*x^2-3*x)/((90*x^3+270*x^2)*lo
g(2)^2+(60*x^5+180*x^4+60*x^3-540*x)*log(2)+10*x^7+30*x^6+20*x^5-170*x^3-30*x^2-90*x+270),x, algorithm="fricas
")

[Out]

1/10*(x^2 - 5*x*log(x + 3))/(x^3 + 3*x*log(2) + x - 3)

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Sympy [A]
time = 0.67, size = 41, normalized size = 1.28 \begin {gather*} \frac {x^{2}}{10 x^{3} + x \left (10 + 30 \log {\left (2 \right )}\right ) - 30} - \frac {x \log {\left (x + 3 \right )}}{2 x^{3} + 2 x + 6 x \log {\left (2 \right )} - 6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x**4+30*x**3+15*x+45)*ln(3+x)+(3*x**3-6*x**2)*ln(2)-x**5-8*x**4+x**3-8*x**2-3*x)/((90*x**3+270*
x**2)*ln(2)**2+(60*x**5+180*x**4+60*x**3-540*x)*ln(2)+10*x**7+30*x**6+20*x**5-170*x**3-30*x**2-90*x+270),x)

[Out]

x**2/(10*x**3 + x*(10 + 30*log(2)) - 30) - x*log(x + 3)/(2*x**3 + 2*x + 6*x*log(2) - 6)

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Giac [A]
time = 0.43, size = 39, normalized size = 1.22 \begin {gather*} \frac {x^{2}}{10 \, {\left (x^{3} + 3 \, x \log \left (2\right ) + x - 3\right )}} - \frac {x \log \left (x + 3\right )}{2 \, {\left (x^{3} + 3 \, x \log \left (2\right ) + x - 3\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4+30*x^3+15*x+45)*log(3+x)+(3*x^3-6*x^2)*log(2)-x^5-8*x^4+x^3-8*x^2-3*x)/((90*x^3+270*x^2)*lo
g(2)^2+(60*x^5+180*x^4+60*x^3-540*x)*log(2)+10*x^7+30*x^6+20*x^5-170*x^3-30*x^2-90*x+270),x, algorithm="giac")

[Out]

1/10*x^2/(x^3 + 3*x*log(2) + x - 3) - 1/2*x*log(x + 3)/(x^3 + 3*x*log(2) + x - 3)

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Mupad [B]
time = 9.36, size = 27, normalized size = 0.84 \begin {gather*} \frac {x\,\left (x-5\,\ln \left (x+3\right )\right )}{10\,\left (x+3\,x\,\ln \left (2\right )+x^3-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x - log(x + 3)*(15*x + 30*x^3 + 10*x^4 + 45) + log(2)*(6*x^2 - 3*x^3) + 8*x^2 - x^3 + 8*x^4 + x^5)/(lo
g(2)*(60*x^3 - 540*x + 180*x^4 + 60*x^5) - 90*x - 30*x^2 - 170*x^3 + 20*x^5 + 30*x^6 + 10*x^7 + log(2)^2*(270*
x^2 + 90*x^3) + 270),x)

[Out]

(x*(x - 5*log(x + 3)))/(10*(x + 3*x*log(2) + x^3 - 3))

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