Optimal. Leaf size=60 \[ -\frac{481 \log \left (x^2+x+1\right )}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left (\frac{2 x+1}{\sqrt{3}}\right )}{2793 \sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.456796, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.192 \[ -\frac{481 \log \left (x^2+x+1\right )}{5586}-\frac{79}{273 (x+5)}+\frac{200 \log (3-2 x)}{3211}+\frac{2731 \log (x+5)}{24843}+\frac{451 \tan ^{-1}\left (\frac{2 x+1}{\sqrt{3}}\right )}{2793 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(1 + 16*x)/((5 + x)^2*(-3 + 2*x)*(1 + x + x^2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 164.427, size = 60, normalized size = 1. \[ \frac{200 \log{\left (- 2 x + 3 \right )}}{3211} + \frac{2731 \log{\left (x + 5 \right )}}{24843} - \frac{481 \log{\left (x^{2} + x + 1 \right )}}{5586} + \frac{451 \sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{2 x}{3} + \frac{1}{3}\right ) \right )}}{8379} - \frac{79}{273 \left (x + 5\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+16*x)/(5+x)**2/(-3+2*x)/(x**2+x+1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0896317, size = 54, normalized size = 0.9 \[ \frac{-243867 \log \left (x^2+x+1\right )-\frac{819546}{x+5}+176400 \log (3-2 x)+311334 \log (x+5)+152438 \sqrt{3} \tan ^{-1}\left (\frac{2 x+1}{\sqrt{3}}\right )}{2832102} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 16*x)/((5 + x)^2*(-3 + 2*x)*(1 + x + x^2)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 48, normalized size = 0.8 \[ -{\frac{481\,\ln \left ({x}^{2}+x+1 \right ) }{5586}}+{\frac{451\,\sqrt{3}}{8379}\arctan \left ({\frac{ \left ( 1+2\,x \right ) \sqrt{3}}{3}} \right ) }-{\frac{79}{1365+273\,x}}+{\frac{2731\,\ln \left ( 5+x \right ) }{24843}}+{\frac{200\,\ln \left ( -3+2\,x \right ) }{3211}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+16*x)/(5+x)^2/(-3+2*x)/(x^2+x+1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.900518, size = 63, normalized size = 1.05 \[ \frac{451}{8379} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x + 1\right )}\right ) - \frac{79}{273 \,{\left (x + 5\right )}} - \frac{481}{5586} \, \log \left (x^{2} + x + 1\right ) + \frac{200}{3211} \, \log \left (2 \, x - 3\right ) + \frac{2731}{24843} \, \log \left (x + 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((16*x + 1)/((x^2 + x + 1)*(2*x - 3)*(x + 5)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.295344, size = 99, normalized size = 1.65 \[ -\frac{\sqrt{3}{\left (81289 \, \sqrt{3}{\left (x + 5\right )} \log \left (x^{2} + x + 1\right ) - 58800 \, \sqrt{3}{\left (x + 5\right )} \log \left (2 \, x - 3\right ) - 103778 \, \sqrt{3}{\left (x + 5\right )} \log \left (x + 5\right ) - 152438 \,{\left (x + 5\right )} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x + 1\right )}\right ) + 273182 \, \sqrt{3}\right )}}{2832102 \,{\left (x + 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((16*x + 1)/((x^2 + x + 1)*(2*x - 3)*(x + 5)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.762493, size = 63, normalized size = 1.05 \[ \frac{200 \log{\left (x - \frac{3}{2} \right )}}{3211} + \frac{2731 \log{\left (x + 5 \right )}}{24843} - \frac{481 \log{\left (x^{2} + x + 1 \right )}}{5586} + \frac{451 \sqrt{3} \operatorname{atan}{\left (\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right )}}{8379} - \frac{79}{273 x + 1365} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+16*x)/(5+x)**2/(-3+2*x)/(x**2+x+1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.263523, size = 81, normalized size = 1.35 \[ \frac{451}{8379} \, \sqrt{3} \arctan \left (-\sqrt{3}{\left (\frac{14}{x + 5} - 3\right )}\right ) - \frac{79}{273 \,{\left (x + 5\right )}} - \frac{481}{5586} \,{\rm ln}\left (-\frac{9}{x + 5} + \frac{21}{{\left (x + 5\right )}^{2}} + 1\right ) + \frac{200}{3211} \,{\rm ln}\left ({\left | -\frac{13}{x + 5} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((16*x + 1)/((x^2 + x + 1)*(2*x - 3)*(x + 5)^2),x, algorithm="giac")
[Out]